# Has a new prime number formula been discovered?

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Something that should be punched into college computing systems although out the nation:<br><br>

If m is a counting number, of the set 1,2,3etc and m=n-1

And we assume that (-1) (-1) always equals = -1 (and is not equal to 1)

Then (m-n)(m-n) shall always equal the negative opposite of a prime or relitively prime number!

A prime number being one that is only divisible by itself and the number one!

A relative prime being the number that can only be expressed as the product of two primes and no more.

Examples:

(1-2)(1-2)=1-2-2-4=-7 (prime)

(2-3)(2-3)=4-6-6-9=-13 (prime)

(3-4)(3-4)=9-12-12-16=-31 (prime)

(4-5)(4-5)=16-20-20-25=-49 (relative prime (-7)*7)

(5-6)(5-6)=25-30-30-36=-71 (prime)

(6-7)(6-7)=36-42-42-49=-97 (prime)

(7-8)(7-8)=49-56-56-64=-127 (prime)

(8-9)(8-9)=64-72-72-81=-161 (relative prime (-7)*23)

(9-10)(9-10)=81-90-90-100=-199 (prime)

(10-11)(10-11)=100-110-110-121=-241 (prime)

(11-12)(11-12)=121-132-132-144=-287 (relative prime (-7)*41

(12-13)(12-13)=144-156-156-169=-337 (prime)

(13-14)(13-14)=169-182-182-196=-391 (relative prime (-17)*23)

So far all the relative primes are divisible by 7 with the other factor being a prime. except for the 13 result. Unfortunately the 4th product and 8th product are relative while the 12th not being so, but this happening on the 11th.

The 13th result being -391 which is equal to 17*23 not being a factor of 7 either.

What pattern the relatives fall under the primes do not, is not yet answerable. If you can compute futher, please post the results below here.

Edited by Realintruder
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You can use: m*m - m*n - m*n - n*n

instead of needing an additional rule for multiplying a negative by a negative.

1st 1000:

The result of: -1 and 0 is 1
The result of: 0 and 1 is -1
The result of: 1 and 2 is -7
The result of: 2 and 3 is -17
The result of: 3 and 4 is -31
The result of: 4 and 5 is -49
The result of: 5 and 6 is -71
The result of: 6 and 7 is -97
The result of: 7 and 8 is -127
The result of: 8 and 9 is -161
The result of: 9 and 10 is -199
The result of: 10 and 11 is -241
The result of: 11 and 12 is -287
The result of: 12 and 13 is -337
The result of: 13 and 14 is -391
The result of: 14 and 15 is -449
The result of: 15 and 16 is -511
The result of: 16 and 17 is -577
The result of: 17 and 18 is -647
The result of: 18 and 19 is -721
The result of: 19 and 20 is -799
The result of: 20 and 21 is -881
The result of: 21 and 22 is -967
The result of: 22 and 23 is -1057
The result of: 23 and 24 is -1151
The result of: 24 and 25 is -1249
The result of: 25 and 26 is -1351
The result of: 26 and 27 is -1457
The result of: 27 and 28 is -1567
The result of: 28 and 29 is -1681
The result of: 29 and 30 is -1799
The result of: 30 and 31 is -1921
The result of: 31 and 32 is -2047
The result of: 32 and 33 is -2177
The result of: 33 and 34 is -2311
The result of: 34 and 35 is -2449
The result of: 35 and 36 is -2591
The result of: 36 and 37 is -2737
The result of: 37 and 38 is -2887
The result of: 38 and 39 is -3041
The result of: 39 and 40 is -3199
The result of: 40 and 41 is -3361
The result of: 41 and 42 is -3527
The result of: 42 and 43 is -3697
The result of: 43 and 44 is -3871
The result of: 44 and 45 is -4049
The result of: 45 and 46 is -4231
The result of: 46 and 47 is -4417
The result of: 47 and 48 is -4607
The result of: 48 and 49 is -4801
The result of: 49 and 50 is -4999
The result of: 50 and 51 is -5201
The result of: 51 and 52 is -5407
The result of: 52 and 53 is -5617
The result of: 53 and 54 is -5831
The result of: 54 and 55 is -6049
The result of: 55 and 56 is -6271
The result of: 56 and 57 is -6497
The result of: 57 and 58 is -6727
The result of: 58 and 59 is -6961
The result of: 59 and 60 is -7199
The result of: 60 and 61 is -7441
The result of: 61 and 62 is -7687
The result of: 62 and 63 is -7937
The result of: 63 and 64 is -8191
The result of: 64 and 65 is -8449
The result of: 65 and 66 is -8711
The result of: 66 and 67 is -8977
The result of: 67 and 68 is -9247
The result of: 68 and 69 is -9521
The result of: 69 and 70 is -9799
The result of: 70 and 71 is -10081
The result of: 71 and 72 is -10367
The result of: 72 and 73 is -10657
The result of: 73 and 74 is -10951
The result of: 74 and 75 is -11249
The result of: 75 and 76 is -11551
The result of: 76 and 77 is -11857
The result of: 77 and 78 is -12167
The result of: 78 and 79 is -12481
The result of: 79 and 80 is -12799
The result of: 80 and 81 is -13121
The result of: 81 and 82 is -13447
The result of: 82 and 83 is -13777
The result of: 83 and 84 is -14111
The result of: 84 and 85 is -14449
The result of: 85 and 86 is -14791
The result of: 86 and 87 is -15137
The result of: 87 and 88 is -15487
The result of: 88 and 89 is -15841
The result of: 89 and 90 is -16199
The result of: 90 and 91 is -16561
The result of: 91 and 92 is -16927
The result of: 92 and 93 is -17297
The result of: 93 and 94 is -17671
The result of: 94 and 95 is -18049
The result of: 95 and 96 is -18431
The result of: 96 and 97 is -18817
The result of: 97 and 98 is -19207
The result of: 98 and 99 is -19601
The result of: 99 and 100 is -19999
The result of: 100 and 101 is -20401
The result of: 101 and 102 is -20807
The result of: 102 and 103 is -21217
The result of: 103 and 104 is -21631
The result of: 104 and 105 is -22049
The result of: 105 and 106 is -22471
The result of: 106 and 107 is -22897
The result of: 107 and 108 is -23327
The result of: 108 and 109 is -23761
The result of: 109 and 110 is -24199
The result of: 110 and 111 is -24641
The result of: 111 and 112 is -25087
The result of: 112 and 113 is -25537
The result of: 113 and 114 is -25991
The result of: 114 and 115 is -26449
The result of: 115 and 116 is -26911
The result of: 116 and 117 is -27377
The result of: 117 and 118 is -27847
The result of: 118 and 119 is -28321
The result of: 119 and 120 is -28799
The result of: 120 and 121 is -29281
The result of: 121 and 122 is -29767
The result of: 122 and 123 is -30257
The result of: 123 and 124 is -30751
The result of: 124 and 125 is -31249
The result of: 125 and 126 is -31751
The result of: 126 and 127 is -32257
The result of: 127 and 128 is -32767
The result of: 128 and 129 is -33281
The result of: 129 and 130 is -33799
The result of: 130 and 131 is -34321
The result of: 131 and 132 is -34847
The result of: 132 and 133 is -35377
The result of: 133 and 134 is -35911
The result of: 134 and 135 is -36449
The result of: 135 and 136 is -36991
The result of: 136 and 137 is -37537
The result of: 137 and 138 is -38087
The result of: 138 and 139 is -38641
The result of: 139 and 140 is -39199
The result of: 140 and 141 is -39761
The result of: 141 and 142 is -40327
The result of: 142 and 143 is -40897
The result of: 143 and 144 is -41471
The result of: 144 and 145 is -42049
The result of: 145 and 146 is -42631
The result of: 146 and 147 is -43217
The result of: 147 and 148 is -43807
The result of: 148 and 149 is -44401
The result of: 149 and 150 is -44999
The result of: 150 and 151 is -45601
The result of: 151 and 152 is -46207
The result of: 152 and 153 is -46817
The result of: 153 and 154 is -47431
The result of: 154 and 155 is -48049
The result of: 155 and 156 is -48671
The result of: 156 and 157 is -49297
The result of: 157 and 158 is -49927
The result of: 158 and 159 is -50561
The result of: 159 and 160 is -51199
The result of: 160 and 161 is -51841
The result of: 161 and 162 is -52487
The result of: 162 and 163 is -53137
The result of: 163 and 164 is -53791
The result of: 164 and 165 is -54449
The result of: 165 and 166 is -55111
The result of: 166 and 167 is -55777
The result of: 167 and 168 is -56447
The result of: 168 and 169 is -57121
The result of: 169 and 170 is -57799
The result of: 170 and 171 is -58481
The result of: 171 and 172 is -59167
The result of: 172 and 173 is -59857
The result of: 173 and 174 is -60551
The result of: 174 and 175 is -61249
The result of: 175 and 176 is -61951
The result of: 176 and 177 is -62657
The result of: 177 and 178 is -63367
The result of: 178 and 179 is -64081
The result of: 179 and 180 is -64799
The result of: 180 and 181 is -65521
The result of: 181 and 182 is -66247
The result of: 182 and 183 is -66977
The result of: 183 and 184 is -67711
The result of: 184 and 185 is -68449
The result of: 185 and 186 is -69191
The result of: 186 and 187 is -69937
The result of: 187 and 188 is -70687
The result of: 188 and 189 is -71441
The result of: 189 and 190 is -72199
The result of: 190 and 191 is -72961
The result of: 191 and 192 is -73727
The result of: 192 and 193 is -74497
The result of: 193 and 194 is -75271
The result of: 194 and 195 is -76049
The result of: 195 and 196 is -76831
The result of: 196 and 197 is -77617
The result of: 197 and 198 is -78407
The result of: 198 and 199 is -79201
The result of: 199 and 200 is -79999
The result of: 200 and 201 is -80801
The result of: 201 and 202 is -81607
The result of: 202 and 203 is -82417
The result of: 203 and 204 is -83231
The result of: 204 and 205 is -84049
The result of: 205 and 206 is -84871
The result of: 206 and 207 is -85697
The result of: 207 and 208 is -86527
The result of: 208 and 209 is -87361
The result of: 209 and 210 is -88199
The result of: 210 and 211 is -89041
The result of: 211 and 212 is -89887
The result of: 212 and 213 is -90737
The result of: 213 and 214 is -91591
The result of: 214 and 215 is -92449
The result of: 215 and 216 is -93311
The result of: 216 and 217 is -94177
The result of: 217 and 218 is -95047
The result of: 218 and 219 is -95921
The result of: 219 and 220 is -96799
The result of: 220 and 221 is -97681
The result of: 221 and 222 is -98567
The result of: 222 and 223 is -99457
The result of: 223 and 224 is -100351
The result of: 224 and 225 is -101249
The result of: 225 and 226 is -102151
The result of: 226 and 227 is -103057
The result of: 227 and 228 is -103967
The result of: 228 and 229 is -104881
The result of: 229 and 230 is -105799
The result of: 230 and 231 is -106721
The result of: 231 and 232 is -107647
The result of: 232 and 233 is -108577
The result of: 233 and 234 is -109511
The result of: 234 and 235 is -110449
The result of: 235 and 236 is -111391
The result of: 236 and 237 is -112337
The result of: 237 and 238 is -113287
The result of: 238 and 239 is -114241
The result of: 239 and 240 is -115199
The result of: 240 and 241 is -116161
The result of: 241 and 242 is -117127
The result of: 242 and 243 is -118097
The result of: 243 and 244 is -119071
The result of: 244 and 245 is -120049
The result of: 245 and 246 is -121031
The result of: 246 and 247 is -122017
The result of: 247 and 248 is -123007
The result of: 248 and 249 is -124001
The result of: 249 and 250 is -124999
The result of: 250 and 251 is -126001
The result of: 251 and 252 is -127007
The result of: 252 and 253 is -128017
The result of: 253 and 254 is -129031
The result of: 254 and 255 is -130049
The result of: 255 and 256 is -131071
The result of: 256 and 257 is -132097
The result of: 257 and 258 is -133127
The result of: 258 and 259 is -134161
The result of: 259 and 260 is -135199
The result of: 260 and 261 is -136241
The result of: 261 and 262 is -137287
The result of: 262 and 263 is -138337
The result of: 263 and 264 is -139391
The result of: 264 and 265 is -140449
The result of: 265 and 266 is -141511
The result of: 266 and 267 is -142577
The result of: 267 and 268 is -143647
The result of: 268 and 269 is -144721
The result of: 269 and 270 is -145799
The result of: 270 and 271 is -146881
The result of: 271 and 272 is -147967
The result of: 272 and 273 is -149057
The result of: 273 and 274 is -150151
The result of: 274 and 275 is -151249
The result of: 275 and 276 is -152351
The result of: 276 and 277 is -153457
The result of: 277 and 278 is -154567
The result of: 278 and 279 is -155681
The result of: 279 and 280 is -156799
The result of: 280 and 281 is -157921
The result of: 281 and 282 is -159047
The result of: 282 and 283 is -160177
The result of: 283 and 284 is -161311
The result of: 284 and 285 is -162449
The result of: 285 and 286 is -163591
The result of: 286 and 287 is -164737
The result of: 287 and 288 is -165887
The result of: 288 and 289 is -167041
The result of: 289 and 290 is -168199
The result of: 290 and 291 is -169361
The result of: 291 and 292 is -170527
The result of: 292 and 293 is -171697
The result of: 293 and 294 is -172871
The result of: 294 and 295 is -174049
The result of: 295 and 296 is -175231
The result of: 296 and 297 is -176417
The result of: 297 and 298 is -177607
The result of: 298 and 299 is -178801
The result of: 299 and 300 is -179999
The result of: 300 and 301 is -181201
The result of: 301 and 302 is -182407
The result of: 302 and 303 is -183617
The result of: 303 and 304 is -184831
The result of: 304 and 305 is -186049
The result of: 305 and 306 is -187271
The result of: 306 and 307 is -188497
The result of: 307 and 308 is -189727
The result of: 308 and 309 is -190961
The result of: 309 and 310 is -192199
The result of: 310 and 311 is -193441
The result of: 311 and 312 is -194687
The result of: 312 and 313 is -195937
The result of: 313 and 314 is -197191
The result of: 314 and 315 is -198449
The result of: 315 and 316 is -199711
The result of: 316 and 317 is -200977
The result of: 317 and 318 is -202247
The result of: 318 and 319 is -203521
The result of: 319 and 320 is -204799
The result of: 320 and 321 is -206081
The result of: 321 and 322 is -207367
The result of: 322 and 323 is -208657
The result of: 323 and 324 is -209951
The result of: 324 and 325 is -211249
The result of: 325 and 326 is -212551
The result of: 326 and 327 is -213857
The result of: 327 and 328 is -215167
The result of: 328 and 329 is -216481
The result of: 329 and 330 is -217799
The result of: 330 and 331 is -219121
The result of: 331 and 332 is -220447
The result of: 332 and 333 is -221777
The result of: 333 and 334 is -223111
The result of: 334 and 335 is -224449
The result of: 335 and 336 is -225791
The result of: 336 and 337 is -227137
The result of: 337 and 338 is -228487
The result of: 338 and 339 is -229841
The result of: 339 and 340 is -231199
The result of: 340 and 341 is -232561
The result of: 341 and 342 is -233927
The result of: 342 and 343 is -235297
The result of: 343 and 344 is -236671
The result of: 344 and 345 is -238049
The result of: 345 and 346 is -239431
The result of: 346 and 347 is -240817
The result of: 347 and 348 is -242207
The result of: 348 and 349 is -243601
The result of: 349 and 350 is -244999
The result of: 350 and 351 is -246401
The result of: 351 and 352 is -247807
The result of: 352 and 353 is -249217
The result of: 353 and 354 is -250631
The result of: 354 and 355 is -252049
The result of: 355 and 356 is -253471
The result of: 356 and 357 is -254897
The result of: 357 and 358 is -256327
The result of: 358 and 359 is -257761
The result of: 359 and 360 is -259199
The result of: 360 and 361 is -260641
The result of: 361 and 362 is -262087
The result of: 362 and 363 is -263537
The result of: 363 and 364 is -264991
The result of: 364 and 365 is -266449
The result of: 365 and 366 is -267911
The result of: 366 and 367 is -269377
The result of: 367 and 368 is -270847
The result of: 368 and 369 is -272321
The result of: 369 and 370 is -273799
The result of: 370 and 371 is -275281
The result of: 371 and 372 is -276767
The result of: 372 and 373 is -278257
The result of: 373 and 374 is -279751
The result of: 374 and 375 is -281249
The result of: 375 and 376 is -282751
The result of: 376 and 377 is -284257
The result of: 377 and 378 is -285767
The result of: 378 and 379 is -287281
The result of: 379 and 380 is -288799
The result of: 380 and 381 is -290321
The result of: 381 and 382 is -291847
The result of: 382 and 383 is -293377
The result of: 383 and 384 is -294911
The result of: 384 and 385 is -296449
The result of: 385 and 386 is -297991
The result of: 386 and 387 is -299537
The result of: 387 and 388 is -301087
The result of: 388 and 389 is -302641
The result of: 389 and 390 is -304199
The result of: 390 and 391 is -305761
The result of: 391 and 392 is -307327
The result of: 392 and 393 is -308897
The result of: 393 and 394 is -310471
The result of: 394 and 395 is -312049
The result of: 395 and 396 is -313631
The result of: 396 and 397 is -315217
The result of: 397 and 398 is -316807
The result of: 398 and 399 is -318401
The result of: 399 and 400 is -319999
The result of: 400 and 401 is -321601
The result of: 401 and 402 is -323207
The result of: 402 and 403 is -324817
The result of: 403 and 404 is -326431
The result of: 404 and 405 is -328049
The result of: 405 and 406 is -329671
The result of: 406 and 407 is -331297
The result of: 407 and 408 is -332927
The result of: 408 and 409 is -334561
The result of: 409 and 410 is -336199
The result of: 410 and 411 is -337841
The result of: 411 and 412 is -339487
The result of: 412 and 413 is -341137
The result of: 413 and 414 is -342791
The result of: 414 and 415 is -344449
The result of: 415 and 416 is -346111
The result of: 416 and 417 is -347777
The result of: 417 and 418 is -349447
The result of: 418 and 419 is -351121
The result of: 419 and 420 is -352799
The result of: 420 and 421 is -354481
The result of: 421 and 422 is -356167
The result of: 422 and 423 is -357857
The result of: 423 and 424 is -359551
The result of: 424 and 425 is -361249
The result of: 425 and 426 is -362951
The result of: 426 and 427 is -364657
The result of: 427 and 428 is -366367
The result of: 428 and 429 is -368081
The result of: 429 and 430 is -369799
The result of: 430 and 431 is -371521
The result of: 431 and 432 is -373247
The result of: 432 and 433 is -374977
The result of: 433 and 434 is -376711
The result of: 434 and 435 is -378449
The result of: 435 and 436 is -380191
The result of: 436 and 437 is -381937
The result of: 437 and 438 is -383687
The result of: 438 and 439 is -385441
The result of: 439 and 440 is -387199
The result of: 440 and 441 is -388961
The result of: 441 and 442 is -390727
The result of: 442 and 443 is -392497
The result of: 443 and 444 is -394271
The result of: 444 and 445 is -396049
The result of: 445 and 446 is -397831
The result of: 446 and 447 is -399617
The result of: 447 and 448 is -401407
The result of: 448 and 449 is -403201
The result of: 449 and 450 is -404999
The result of: 450 and 451 is -406801
The result of: 451 and 452 is -408607
The result of: 452 and 453 is -410417
The result of: 453 and 454 is -412231
The result of: 454 and 455 is -414049
The result of: 455 and 456 is -415871
The result of: 456 and 457 is -417697
The result of: 457 and 458 is -419527
The result of: 458 and 459 is -421361
The result of: 459 and 460 is -423199
The result of: 460 and 461 is -425041
The result of: 461 and 462 is -426887
The result of: 462 and 463 is -428737
The result of: 463 and 464 is -430591
The result of: 464 and 465 is -432449
The result of: 465 and 466 is -434311
The result of: 466 and 467 is -436177
The result of: 467 and 468 is -438047
The result of: 468 and 469 is -439921
The result of: 469 and 470 is -441799
The result of: 470 and 471 is -443681
The result of: 471 and 472 is -445567
The result of: 472 and 473 is -447457
The result of: 473 and 474 is -449351
The result of: 474 and 475 is -451249
The result of: 475 and 476 is -453151
The result of: 476 and 477 is -455057
The result of: 477 and 478 is -456967
The result of: 478 and 479 is -458881
The result of: 479 and 480 is -460799
The result of: 480 and 481 is -462721
The result of: 481 and 482 is -464647
The result of: 482 and 483 is -466577
The result of: 483 and 484 is -468511
The result of: 484 and 485 is -470449
The result of: 485 and 486 is -472391
The result of: 486 and 487 is -474337
The result of: 487 and 488 is -476287
The result of: 488 and 489 is -478241
The result of: 489 and 490 is -480199
The result of: 490 and 491 is -482161
The result of: 491 and 492 is -484127
The result of: 492 and 493 is -486097
The result of: 493 and 494 is -488071
The result of: 494 and 495 is -490049
The result of: 495 and 496 is -492031
The result of: 496 and 497 is -494017
The result of: 497 and 498 is -496007
The result of: 498 and 499 is -498001
The result of: 499 and 500 is -499999
The result of: 500 and 501 is -502001
The result of: 501 and 502 is -504007
The result of: 502 and 503 is -506017
The result of: 503 and 504 is -508031
The result of: 504 and 505 is -510049
The result of: 505 and 506 is -512071
The result of: 506 and 507 is -514097
The result of: 507 and 508 is -516127
The result of: 508 and 509 is -518161
The result of: 509 and 510 is -520199
The result of: 510 and 511 is -522241
The result of: 511 and 512 is -524287
The result of: 512 and 513 is -526337
The result of: 513 and 514 is -528391
The result of: 514 and 515 is -530449
The result of: 515 and 516 is -532511
The result of: 516 and 517 is -534577
The result of: 517 and 518 is -536647
The result of: 518 and 519 is -538721
The result of: 519 and 520 is -540799
The result of: 520 and 521 is -542881
The result of: 521 and 522 is -544967
The result of: 522 and 523 is -547057
The result of: 523 and 524 is -549151
The result of: 524 and 525 is -551249
The result of: 525 and 526 is -553351
The result of: 526 and 527 is -555457
The result of: 527 and 528 is -557567
The result of: 528 and 529 is -559681
The result of: 529 and 530 is -561799
The result of: 530 and 531 is -563921
The result of: 531 and 532 is -566047
The result of: 532 and 533 is -568177
The result of: 533 and 534 is -570311
The result of: 534 and 535 is -572449
The result of: 535 and 536 is -574591
The result of: 536 and 537 is -576737
The result of: 537 and 538 is -578887
The result of: 538 and 539 is -581041
The result of: 539 and 540 is -583199
The result of: 540 and 541 is -585361
The result of: 541 and 542 is -587527
The result of: 542 and 543 is -589697
The result of: 543 and 544 is -591871
The result of: 544 and 545 is -594049
The result of: 545 and 546 is -596231
The result of: 546 and 547 is -598417
The result of: 547 and 548 is -600607
The result of: 548 and 549 is -602801
The result of: 549 and 550 is -604999
The result of: 550 and 551 is -607201
The result of: 551 and 552 is -609407
The result of: 552 and 553 is -611617
The result of: 553 and 554 is -613831
The result of: 554 and 555 is -616049
The result of: 555 and 556 is -618271
The result of: 556 and 557 is -620497
The result of: 557 and 558 is -622727
The result of: 558 and 559 is -624961
The result of: 559 and 560 is -627199
The result of: 560 and 561 is -629441
The result of: 561 and 562 is -631687
The result of: 562 and 563 is -633937
The result of: 563 and 564 is -636191
The result of: 564 and 565 is -638449
The result of: 565 and 566 is -640711
The result of: 566 and 567 is -642977
The result of: 567 and 568 is -645247
The result of: 568 and 569 is -647521
The result of: 569 and 570 is -649799
The result of: 570 and 571 is -652081
The result of: 571 and 572 is -654367
The result of: 572 and 573 is -656657
The result of: 573 and 574 is -658951
The result of: 574 and 575 is -661249
The result of: 575 and 576 is -663551
The result of: 576 and 577 is -665857
The result of: 577 and 578 is -668167
The result of: 578 and 579 is -670481
The result of: 579 and 580 is -672799
The result of: 580 and 581 is -675121
The result of: 581 and 582 is -677447
The result of: 582 and 583 is -679777
The result of: 583 and 584 is -682111
The result of: 584 and 585 is -684449
The result of: 585 and 586 is -686791
The result of: 586 and 587 is -689137
The result of: 587 and 588 is -691487
The result of: 588 and 589 is -693841
The result of: 589 and 590 is -696199
The result of: 590 and 591 is -698561
The result of: 591 and 592 is -700927
The result of: 592 and 593 is -703297
The result of: 593 and 594 is -705671
The result of: 594 and 595 is -708049
The result of: 595 and 596 is -710431
The result of: 596 and 597 is -712817
The result of: 597 and 598 is -715207
The result of: 598 and 599 is -717601
The result of: 599 and 600 is -719999
The result of: 600 and 601 is -722401
The result of: 601 and 602 is -724807
The result of: 602 and 603 is -727217
The result of: 603 and 604 is -729631
The result of: 604 and 605 is -732049
The result of: 605 and 606 is -734471
The result of: 606 and 607 is -736897
The result of: 607 and 608 is -739327
The result of: 608 and 609 is -741761
The result of: 609 and 610 is -744199
The result of: 610 and 611 is -746641
The result of: 611 and 612 is -749087
The result of: 612 and 613 is -751537
The result of: 613 and 614 is -753991
The result of: 614 and 615 is -756449
The result of: 615 and 616 is -758911
The result of: 616 and 617 is -761377
The result of: 617 and 618 is -763847
The result of: 618 and 619 is -766321
The result of: 619 and 620 is -768799
The result of: 620 and 621 is -771281
The result of: 621 and 622 is -773767
The result of: 622 and 623 is -776257
The result of: 623 and 624 is -778751
The result of: 624 and 625 is -781249
The result of: 625 and 626 is -783751
The result of: 626 and 627 is -786257
The result of: 627 and 628 is -788767
The result of: 628 and 629 is -791281
The result of: 629 and 630 is -793799
The result of: 630 and 631 is -796321
The result of: 631 and 632 is -798847
The result of: 632 and 633 is -801377
The result of: 633 and 634 is -803911
The result of: 634 and 635 is -806449
The result of: 635 and 636 is -808991
The result of: 636 and 637 is -811537
The result of: 637 and 638 is -814087
The result of: 638 and 639 is -816641
The result of: 639 and 640 is -819199
The result of: 640 and 641 is -821761
The result of: 641 and 642 is -824327
The result of: 642 and 643 is -826897
The result of: 643 and 644 is -829471
The result of: 644 and 645 is -832049
The result of: 645 and 646 is -834631
The result of: 646 and 647 is -837217
The result of: 647 and 648 is -839807
The result of: 648 and 649 is -842401
The result of: 649 and 650 is -844999
The result of: 650 and 651 is -847601
The result of: 651 and 652 is -850207
The result of: 652 and 653 is -852817
The result of: 653 and 654 is -855431
The result of: 654 and 655 is -858049
The result of: 655 and 656 is -860671
The result of: 656 and 657 is -863297
The result of: 657 and 658 is -865927
The result of: 658 and 659 is -868561
The result of: 659 and 660 is -871199
The result of: 660 and 661 is -873841
The result of: 661 and 662 is -876487
The result of: 662 and 663 is -879137
The result of: 663 and 664 is -881791
The result of: 664 and 665 is -884449
The result of: 665 and 666 is -887111
The result of: 666 and 667 is -889777
The result of: 667 and 668 is -892447
The result of: 668 and 669 is -895121
The result of: 669 and 670 is -897799
The result of: 670 and 671 is -900481
The result of: 671 and 672 is -903167
The result of: 672 and 673 is -905857
The result of: 673 and 674 is -908551
The result of: 674 and 675 is -911249
The result of: 675 and 676 is -913951
The result of: 676 and 677 is -916657
The result of: 677 and 678 is -919367
The result of: 678 and 679 is -922081
The result of: 679 and 680 is -924799
The result of: 680 and 681 is -927521
The result of: 681 and 682 is -930247
The result of: 682 and 683 is -932977
The result of: 683 and 684 is -935711
The result of: 684 and 685 is -938449
The result of: 685 and 686 is -941191
The result of: 686 and 687 is -943937
The result of: 687 and 688 is -946687
The result of: 688 and 689 is -949441
The result of: 689 and 690 is -952199
The result of: 690 and 691 is -954961
The result of: 691 and 692 is -957727
The result of: 692 and 693 is -960497
The result of: 693 and 694 is -963271
The result of: 694 and 695 is -966049
The result of: 695 and 696 is -968831
The result of: 696 and 697 is -971617
The result of: 697 and 698 is -974407
The result of: 698 and 699 is -977201
The result of: 699 and 700 is -979999
The result of: 700 and 701 is -982801
The result of: 701 and 702 is -985607
The result of: 702 and 703 is -988417
The result of: 703 and 704 is -991231
The result of: 704 and 705 is -994049
The result of: 705 and 706 is -996871
The result of: 706 and 707 is -999697
The result of: 707 and 708 is -1002527
The result of: 708 and 709 is -1005361
The result of: 709 and 710 is -1008199
The result of: 710 and 711 is -1011041
The result of: 711 and 712 is -1013887
The result of: 712 and 713 is -1016737
The result of: 713 and 714 is -1019591
The result of: 714 and 715 is -1022449
The result of: 715 and 716 is -1025311
The result of: 716 and 717 is -1028177
The result of: 717 and 718 is -1031047
The result of: 718 and 719 is -1033921
The result of: 719 and 720 is -1036799
The result of: 720 and 721 is -1039681
The result of: 721 and 722 is -1042567
The result of: 722 and 723 is -1045457
The result of: 723 and 724 is -1048351
The result of: 724 and 725 is -1051249
The result of: 725 and 726 is -1054151
The result of: 726 and 727 is -1057057
The result of: 727 and 728 is -1059967
The result of: 728 and 729 is -1062881
The result of: 729 and 730 is -1065799
The result of: 730 and 731 is -1068721
The result of: 731 and 732 is -1071647
The result of: 732 and 733 is -1074577
The result of: 733 and 734 is -1077511
The result of: 734 and 735 is -1080449
The result of: 735 and 736 is -1083391
The result of: 736 and 737 is -1086337
The result of: 737 and 738 is -1089287
The result of: 738 and 739 is -1092241
The result of: 739 and 740 is -1095199
The result of: 740 and 741 is -1098161
The result of: 741 and 742 is -1101127
The result of: 742 and 743 is -1104097
The result of: 743 and 744 is -1107071
The result of: 744 and 745 is -1110049
The result of: 745 and 746 is -1113031
The result of: 746 and 747 is -1116017
The result of: 747 and 748 is -1119007
The result of: 748 and 749 is -1122001
The result of: 749 and 750 is -1124999
The result of: 750 and 751 is -1128001
The result of: 751 and 752 is -1131007
The result of: 752 and 753 is -1134017
The result of: 753 and 754 is -1137031
The result of: 754 and 755 is -1140049
The result of: 755 and 756 is -1143071
The result of: 756 and 757 is -1146097
The result of: 757 and 758 is -1149127
The result of: 758 and 759 is -1152161
The result of: 759 and 760 is -1155199
The result of: 760 and 761 is -1158241
The result of: 761 and 762 is -1161287
The result of: 762 and 763 is -1164337
The result of: 763 and 764 is -1167391
The result of: 764 and 765 is -1170449
The result of: 765 and 766 is -1173511
The result of: 766 and 767 is -1176577
The result of: 767 and 768 is -1179647
The result of: 768 and 769 is -1182721
The result of: 769 and 770 is -1185799
The result of: 770 and 771 is -1188881
The result of: 771 and 772 is -1191967
The result of: 772 and 773 is -1195057
The result of: 773 and 774 is -1198151
The result of: 774 and 775 is -1201249
The result of: 775 and 776 is -1204351
The result of: 776 and 777 is -1207457
The result of: 777 and 778 is -1210567
The result of: 778 and 779 is -1213681
The result of: 779 and 780 is -1216799
The result of: 780 and 781 is -1219921
The result of: 781 and 782 is -1223047
The result of: 782 and 783 is -1226177
The result of: 783 and 784 is -1229311
The result of: 784 and 785 is -1232449
The result of: 785 and 786 is -1235591
The result of: 786 and 787 is -1238737
The result of: 787 and 788 is -1241887
The result of: 788 and 789 is -1245041
The result of: 789 and 790 is -1248199
The result of: 790 and 791 is -1251361
The result of: 791 and 792 is -1254527
The result of: 792 and 793 is -1257697
The result of: 793 and 794 is -1260871
The result of: 794 and 795 is -1264049
The result of: 795 and 796 is -1267231
The result of: 796 and 797 is -1270417
The result of: 797 and 798 is -1273607
The result of: 798 and 799 is -1276801
The result of: 799 and 800 is -1279999
The result of: 800 and 801 is -1283201
The result of: 801 and 802 is -1286407
The result of: 802 and 803 is -1289617
The result of: 803 and 804 is -1292831
The result of: 804 and 805 is -1296049
The result of: 805 and 806 is -1299271
The result of: 806 and 807 is -1302497
The result of: 807 and 808 is -1305727
The result of: 808 and 809 is -1308961
The result of: 809 and 810 is -1312199
The result of: 810 and 811 is -1315441
The result of: 811 and 812 is -1318687
The result of: 812 and 813 is -1321937
The result of: 813 and 814 is -1325191
The result of: 814 and 815 is -1328449
The result of: 815 and 816 is -1331711
The result of: 816 and 817 is -1334977
The result of: 817 and 818 is -1338247
The result of: 818 and 819 is -1341521
The result of: 819 and 820 is -1344799
The result of: 820 and 821 is -1348081
The result of: 821 and 822 is -1351367
The result of: 822 and 823 is -1354657
The result of: 823 and 824 is -1357951
The result of: 824 and 825 is -1361249
The result of: 825 and 826 is -1364551
The result of: 826 and 827 is -1367857
The result of: 827 and 828 is -1371167
The result of: 828 and 829 is -1374481
The result of: 829 and 830 is -1377799
The result of: 830 and 831 is -1381121
The result of: 831 and 832 is -1384447
The result of: 832 and 833 is -1387777
The result of: 833 and 834 is -1391111
The result of: 834 and 835 is -1394449
The result of: 835 and 836 is -1397791
The result of: 836 and 837 is -1401137
The result of: 837 and 838 is -1404487
The result of: 838 and 839 is -1407841
The result of: 839 and 840 is -1411199
The result of: 840 and 841 is -1414561
The result of: 841 and 842 is -1417927
The result of: 842 and 843 is -1421297
The result of: 843 and 844 is -1424671
The result of: 844 and 845 is -1428049
The result of: 845 and 846 is -1431431
The result of: 846 and 847 is -1434817
The result of: 847 and 848 is -1438207
The result of: 848 and 849 is -1441601
The result of: 849 and 850 is -1444999
The result of: 850 and 851 is -1448401
The result of: 851 and 852 is -1451807
The result of: 852 and 853 is -1455217
The result of: 853 and 854 is -1458631
The result of: 854 and 855 is -1462049
The result of: 855 and 856 is -1465471
The result of: 856 and 857 is -1468897
The result of: 857 and 858 is -1472327
The result of: 858 and 859 is -1475761
The result of: 859 and 860 is -1479199
The result of: 860 and 861 is -1482641
The result of: 861 and 862 is -1486087
The result of: 862 and 863 is -1489537
The result of: 863 and 864 is -1492991
The result of: 864 and 865 is -1496449
The result of: 865 and 866 is -1499911
The result of: 866 and 867 is -1503377
The result of: 867 and 868 is -1506847
The result of: 868 and 869 is -1510321
The result of: 869 and 870 is -1513799
The result of: 870 and 871 is -1517281
The result of: 871 and 872 is -1520767
The result of: 872 and 873 is -1524257
The result of: 873 and 874 is -1527751
The result of: 874 and 875 is -1531249
The result of: 875 and 876 is -1534751
The result of: 876 and 877 is -1538257
The result of: 877 and 878 is -1541767
The result of: 878 and 879 is -1545281
The result of: 879 and 880 is -1548799
The result of: 880 and 881 is -1552321
The result of: 881 and 882 is -1555847
The result of: 882 and 883 is -1559377
The result of: 883 and 884 is -1562911
The result of: 884 and 885 is -1566449
The result of: 885 and 886 is -1569991
The result of: 886 and 887 is -1573537
The result of: 887 and 888 is -1577087
The result of: 888 and 889 is -1580641
The result of: 889 and 890 is -1584199
The result of: 890 and 891 is -1587761
The result of: 891 and 892 is -1591327
The result of: 892 and 893 is -1594897
The result of: 893 and 894 is -1598471
The result of: 894 and 895 is -1602049
The result of: 895 and 896 is -1605631
The result of: 896 and 897 is -1609217
The result of: 897 and 898 is -1612807
The result of: 898 and 899 is -1616401
The result of: 899 and 900 is -1619999
The result of: 900 and 901 is -1623601
The result of: 901 and 902 is -1627207
The result of: 902 and 903 is -1630817
The result of: 903 and 904 is -1634431
The result of: 904 and 905 is -1638049
The result of: 905 and 906 is -1641671
The result of: 906 and 907 is -1645297
The result of: 907 and 908 is -1648927
The result of: 908 and 909 is -1652561
The result of: 909 and 910 is -1656199
The result of: 910 and 911 is -1659841
The result of: 911 and 912 is -1663487
The result of: 912 and 913 is -1667137
The result of: 913 and 914 is -1670791
The result of: 914 and 915 is -1674449
The result of: 915 and 916 is -1678111
The result of: 916 and 917 is -1681777
The result of: 917 and 918 is -1685447
The result of: 918 and 919 is -1689121
The result of: 919 and 920 is -1692799
The result of: 920 and 921 is -1696481
The result of: 921 and 922 is -1700167
The result of: 922 and 923 is -1703857
The result of: 923 and 924 is -1707551
The result of: 924 and 925 is -1711249
The result of: 925 and 926 is -1714951
The result of: 926 and 927 is -1718657
The result of: 927 and 928 is -1722367
The result of: 928 and 929 is -1726081
The result of: 929 and 930 is -1729799
The result of: 930 and 931 is -1733521
The result of: 931 and 932 is -1737247
The result of: 932 and 933 is -1740977
The result of: 933 and 934 is -1744711
The result of: 934 and 935 is -1748449
The result of: 935 and 936 is -1752191
The result of: 936 and 937 is -1755937
The result of: 937 and 938 is -1759687
The result of: 938 and 939 is -1763441
The result of: 939 and 940 is -1767199
The result of: 940 and 941 is -1770961
The result of: 941 and 942 is -1774727
The result of: 942 and 943 is -1778497
The result of: 943 and 944 is -1782271
The result of: 944 and 945 is -1786049
The result of: 945 and 946 is -1789831
The result of: 946 and 947 is -1793617
The result of: 947 and 948 is -1797407
The result of: 948 and 949 is -1801201
The result of: 949 and 950 is -1804999
The result of: 950 and 951 is -1808801
The result of: 951 and 952 is -1812607
The result of: 952 and 953 is -1816417
The result of: 953 and 954 is -1820231
The result of: 954 and 955 is -1824049
The result of: 955 and 956 is -1827871
The result of: 956 and 957 is -1831697
The result of: 957 and 958 is -1835527
The result of: 958 and 959 is -1839361
The result of: 959 and 960 is -1843199
The result of: 960 and 961 is -1847041
The result of: 961 and 962 is -1850887
The result of: 962 and 963 is -1854737
The result of: 963 and 964 is -1858591
The result of: 964 and 965 is -1862449
The result of: 965 and 966 is -1866311
The result of: 966 and 967 is -1870177
The result of: 967 and 968 is -1874047
The result of: 968 and 969 is -1877921
The result of: 969 and 970 is -1881799
The result of: 970 and 971 is -1885681
The result of: 971 and 972 is -1889567
The result of: 972 and 973 is -1893457
The result of: 973 and 974 is -1897351
The result of: 974 and 975 is -1901249
The result of: 975 and 976 is -1905151
The result of: 976 and 977 is -1909057
The result of: 977 and 978 is -1912967
The result of: 978 and 979 is -1916881
The result of: 979 and 980 is -1920799
The result of: 980 and 981 is -1924721
The result of: 981 and 982 is -1928647
The result of: 982 and 983 is -1932577
The result of: 983 and 984 is -1936511
The result of: 984 and 985 is -1940449
The result of: 985 and 986 is -1944391
The result of: 986 and 987 is -1948337
The result of: 987 and 988 is -1952287
The result of: 988 and 989 is -1956241
The result of: 989 and 990 is -1960199
The result of: 990 and 991 is -1964161
The result of: 991 and 992 is -1968127
The result of: 992 and 993 is -1972097
The result of: 993 and 994 is -1976071
The result of: 994 and 995 is -1980049
The result of: 995 and 996 is -1984031
The result of: 996 and 997 is -1988017
The result of: 997 and 998 is -1992007
The result of: 998 and 999 is -1996001

code utilized:

<!DOCTYPE html>
<html>
<body>

<p>Click the button to run.</p>
<button onclick="myFunction()">Run</button>
<p id="demo"></p>

<script>
function myFunction() {
var x = "", i;
var n = 0;
var m = 0;
var result = 0;
for (i=0; i<1000; i++) {
m = n-1;
result = m*m - m*n - m*n - n*n;

x = x + "The result of: " + m +" and " + n +" is " + result + "<br>";
n++;
}
document.getElementById("demo").innerHTML = x;
}
</script>

</body>
</html>



note: you posted -61 instead of -71 for m=5, n=6

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Thank tou for the advice I will use it.

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Alternatively, just use n2 + 2mn - m2 to yield a positive result. Consider also that since m = n - 1, this is equivalent to n2 + 2(n - 1)n - (n - 1)2 = n2 + 2n2 - 2n - n2 + 2n - 1 = 2n2 - 1.

However, the conjecture does eventually fail. Without going through the large list Endy produced to look for an earlier counterexample, just let n = 1000, and we have 2n2 - 1 = 1999999 = 17(71)(1657).

Edited by John
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Looking at it several of the numbers at the end fall into that same boat. I'm thinking they all may be the end result of the multiplication of one or more prime numbers, but I haven't tested that.

Ironically, 1000 itself is not on the generated list since I started n at 0.

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Well, if I'm understanding your meaning correctly, then there is no need to test. The fundamental theorem of arithmetic guarantees that any integer greater than 1 is either prime or the product of a unique set of primes.

There is at least one restriction on the prime factorization of each end product, though, which is that it cannot contain any of the prime factors of n (and probably of m either, though I'm not as absolutely certain).

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That makes sense. I've studied some of the other puzzles of math(palindromic numbers, division by zero) but hadn't worked with prime numbers to the same degree.

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My formula has not been proven wrong yet. What works to produce the same result is of (-1)(-1) does not equal (-1) but 1 is m^2-2mn-2(mn)^2 as stated in my forum on that link in the bottom of my post.

But if you use m^2-2mm-n^2 as suggested by you for 1,000 you will get 2004001 which is a prime (or relative prime) number. And has no factors but itself and 1.

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My formula has not been proven wrong yet. What works to produce the same result is of (-1)(-1) does not equal (-1) but 1 is m^2-2mn-2(mn)^2 as stated in my forum on that link in the bottom of my post.

If we go by your original post, then we have n = 1000, m = 999. Using the modified multiplication you proposed, then, we have (999-1000)(999-1000) = 998001 - 1998000 - 1000000 = -1999999, which we've shown is a counterexample. So yes, unfortunately, your formula has been proven wrong.

But if you use m^2-2mm-n^2 as suggested by you for 1,000 you will get 2004001 which is a prime (or relative prime) number. And has no factors but itself and 1.

2mn, not 2mm. Even using 2mm, though, this results in -1998001 and not -2004001. You must have made an arithmetic error somewhere.

Edit: Also, I looked at the blog post you linked. At the end, you write:

(m-n)(m-n)-2(mn)^2=m^2-2mn-2(mn)^2

This is not quite correct, since (m-n)(m-n) - 2(mn)2 = m2 - 2mn + n2 - 2(mn)2. That is to say, you left out an n2.

Edited by John
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Yes my therom or theory has been disproven wrong.

Thank You

I wonder if it hold true for all counting numbers less than 1,000.

Have you tested that out?

That would be something.

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