sunshaker 28 Posted May 3, 2017 Share Posted May 3, 2017 Just messing around with primes+30 to give next primes, some +30's do not equal a prime, but if not, they always equal a prime x's a prime? when this happens, I add 30 again, which gives a prime, unless it is once again a prime x's a prime. Example: Prime 19 + 30= 49, not a prime, but a prime x's a prime =7x7=49, but then add 30 again will give me prime 79. So no prime x's prime can equal a prime? why does adding 30 to a prime, always give a prime, unless the answer is a prime x's a prime, but adding 30 again gives a prime? prime plus 30 prime x prime 5 35 5x7 +30=65 = 5x13 +30=95 = 5x19 +30=125=25x5 +30=155 =31x5 +30=185 =19x5 7 37 11 41 13 43 17 47 19 49 7x7 +30=79 23 53 29 59 31 61 37 67 41 71 43 73 47 77 11x7 +30=107 53 83 59 89 61 91 13x7 +30=121 +30=151 67 97 71 101 73 103 79 109 83 113 89 119 17x7 +30=149 97 127 101 131 103 133 19x7 +30=163 107 137 109 139 113 143 13x11 +30=173 127 157 131 161 23x7 +30=191 137 167 139 169 13x13 +30=199 149 179 151 181 157 187 17x11 +30=217 =31x7 +30=247 =19x13 +30=277 163 193 167 197 173 203 29x7 +30=233 179 209 19x11 +30=239 181 211 191 221 17x13 +30=251 193 223 197 227 199 229 211 241 223 253 23x11 +30=283 227 257 229 259 37x7 +30=289= 17x17 +30=329 =47x7 +30=359 233 263 239 269 241 271 251 281 257 287 41x7 +30=317 263 293 Link to post Share on other sites

swansont 7484 Posted May 3, 2017 Share Posted May 3, 2017 2 is prime 2 Link to post Share on other sites

Bender 204 Posted May 3, 2017 Share Posted May 3, 2017 prime plus 30 prime x prime 5 35 5x7 +30=65 = 5x13 +30=95 = 5x19 +30=125=25x5 +30=155 =31x5 +30=185 =19x5 25 is not prime 2 Link to post Share on other sites

Strange 4272 Posted May 3, 2017 Share Posted May 3, 2017 some +30's do not equal a prime, but if not, they always equal a prime x's a prime? All non-primes are the product of primes. 1 Link to post Share on other sites

imatfaal 2481 Posted May 3, 2017 Share Posted May 3, 2017 Strange has definitively answered one of your questions (all numbers are either primes or multiples of primes) this is the Fundamental Theory of Arithmetic The 30 gap thing is to do with the number system - but it is not that useful or interesting. Think on this and it will become obvious: 1. A prime number must be of the form 2w+1 (it must be odd (apart from 2 itself) 2. At the same time the prime must be of the form 3y+1 or 3y+2 (it cannot be divided by 3) 3. Still at the same time the prime must be of the form 5z+1, 5z+2, 5z+3, or 5z+4 (it cannot be divided by 5) 4. This pattern continues with 7, 9 ,11 ,13 etc as the prime grows 5. 30 is 2 x 3 x 5 6. So, if you already have a prime you are adding a simple multiple of 2s, 3s, and 5s to the prime 7. As an example (2w+1) + (2 x 3 x 5) = 2w+1 + 2 x 15 = 2(w+15) + 1 (ie still cannot be divided by 2) 8. This follows for 3 and for 5 9. In short - any number not divisible by 2 ,3 or 5 will when 30 is added still not be divisible You will notice your +30 schema fails as soon as 7s start cropping up. (+210 will work too - but less often) The reason that adding 30 again often gives a prime is that 30 is NOT divisible by any prime greater than 5. So you can know that if your (failed selection) is, for example divisible by 11, then (failed selection +30) CANNOT be divisible by 11. Sooner or later adding 30 a second time will not work, but a third or fourth might. But hopefully you can see that this is not predictive of primes - or it is selectively predictive - but it is kinda obvious when you look at how numbers are made up and not useful because you still have to check 6 Link to post Share on other sites

sunshaker 28 Posted May 3, 2017 Author Share Posted May 3, 2017 2 is prime Yep:),But...,I found it seemed to work after 5, but 2 & 5 would still give me all prime x primes of 2 & 5: 2 x31 5x5 etc. @strange @Imatfaal, Thanks for info, did not fully realize(understand) about unique-prime-factorization theorem, &"composite numbers" where the plus 30 fails 35,49,77 etc, I just found it interesting,that these composite numbers are the product of just "2 primes" that went to a sort of order, 5x7 7x7, 11x7, 13x7, etc, so has i went higher up the primes, I would use 7 & every other prime 7x103, 7x113, 7x131etc. Then 11 and every other prime, Then 13 and ever other prime, etc. But then again it does help if you know your "prime x's tables". cheers anyway, back to drawing board. 1 Link to post Share on other sites

imatfaal 2481 Posted May 4, 2017 Share Posted May 4, 2017 Yep:),But...,I found it seemed to work after 5, but 2 & 5 would still give me all prime x primes of 2 & 5: 2 x31 5x5 etc. @strange @Imatfaal, Thanks for info, did not fully realize(understand) about unique-prime-factorization theorem, &"composite numbers" where the plus 30 fails 35,49,77 etc, I just found it interesting,that these composite numbers are the product of just "2 primes" that went to a sort of order, 5x7 7x7, 11x7, 13x7, etc, so has i went higher up the primes, I would use 7 & every other prime 7x103, 7x113, 7x131etc. Then 11 and every other prime, Then 13 and ever other prime, etc. But then again it does help if you know your "prime x's tables". cheers anyway, back to drawing board. I believe primes have fascinated mathematicians since the time whereof the memory of man knoweth not - they are slippery customers and every time we (even great mathematical colossi) think they have a good handle on them they squirm free. We know a huge amount about them and about factorization - but the holes in our knowledge are annoying and not insignificant. The Mathematical communities main avenue of approach is via the Riemman Zeta function - but that is really gnarly maths 1 Link to post Share on other sites

koti 484 Posted May 4, 2017 Share Posted May 4, 2017 I believe primes have fascinated mathematicians since the time whereof the memory of man knoweth not - they are slippery customers and every time we (even great mathematical colossi) think they have a good handle on them they squirm free. We know a huge amount about them and about factorization - but the holes in our knowledge are annoying and not insignificant. The Mathematical communities main avenue of approach is via the Riemman Zeta function - but that is really gnarly maths Personally, I always found Stanisław Ulam's discovery of the correlation between primes and geometry very fascinating. Link to post Share on other sites

imatfaal 2481 Posted May 5, 2017 Share Posted May 5, 2017 Personally, I always found Stanisław Ulam's discovery of the correlation between primes and geometry very fascinating. A truly great mathematician - in an age in which the competition was tough. There was such a flourishing of mathematical/scientific genius in the 30s and 40s - and it is such a tragedy that the world was forced / allowed itself to use that brilliance to develop weapons. Where would we be as a species if the incredible genius of people like Ulam and the other colossal intellects of the Manhattan project has been free to choose their own goals - yet were still granted the resources, the time, and the ambition and ability to work together. Link to post Share on other sites

koti 484 Posted May 5, 2017 Share Posted May 5, 2017 A truly great mathematician - in an age in which the competition was tough. There was such a flourishing of mathematical/scientific genius in the 30s and 40s - and it is such a tragedy that the world was forced / allowed itself to use that brilliance to develop weapons. Where would we be as a species if the incredible genius of people like Ulam and the other colossal intellects of the Manhattan project has been free to choose their own goals - yet were still granted the resources, the time, and the ambition and ability to work together. I don't think it's possible at least not for a long time but that is a kind of utopia that I would love to live in. Link to post Share on other sites

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