Trurl

Why would he have to be created? We talk about infinity in the forums all the time. How about always was.

For students or amateurs (myself included), I recommend Wikipedia or https://oeis.org/A000040 Here is a great number theory resource that can be imported to Excel or Mathematica. I imported the 1st 1000 Primes into Mathematica. I was very proud until I learned Mathematica had a library built in, in my S.Y.I post. I recommend downloading the notebook file in my post and importing your own file. But the possibility of manipulating numbers on oeis and Wikipedia sites is endless.

No. I am just saying you can’t go back to no weapons. I believe the assault weapons ban that expired only covered new manufacturing. Just like the legalization of weed you can’t fix the problem by making it illegal again. Both are problems. But I am saying if the gun lobbies lose one restriction they know more restrictions will follow. So we can’t agree on any laws. It is important to note, every time a ban on guns is mentioned it only increases sales. We are not in disagreement. I am just stating that is the reason there is no easy fix. We can’t agree on masks or abortion. How can we pass gun control? Make gun control a federal law with universal background checks?

I am not for the sale of assault rifles. But many already own them. You cannot eliminate them. It is a dangerous move to change the Constitution. I know that seems ridiculous. But that is why the gun laws are debated so heavily. If the gun owners concede to one law they will be subjected to more laws eventually leading to loss of all rights. I don’t agree but this is why nothing is done. We need guns to be tied to a psychological program on our cell phone. Just as Google tracks us. Things like gps location, flagged searches, and the psychological profiles that all the data creates. This seems impossible but what if a gun check required your online profile to be searched?

Calvinism vs Arminianism

You must be a scientist. Always striving to discover something new. I too am aligned with the free will side. But there is also compelling arguments for predetermined side. Look at you phone constantly monitoring and influencing you. The question to ask is who controls such events? Is it random? Who would be a separate observer to intentionally influence others? And all these multiverses would not be possible if we had no choice. Now my question is how would we even know determined or fixed. We have a first person perspective and are oblivious to how it works. I just like the discussion. I think I am in control of my decisions, but if you watch the lecture you may doubt the certainty of fee will. But like you free will is good enough for me. I shouldn’t have let that lecture influence me.

I was watching a lecture on the philosophy of science fiction and there was a debate on the movie The Matrix. All about how the trilogy is a debate on free will. If God knows are character and presents us with a decision and knows our response, did we have a choice? And if we didn’t have a choice who is to blame? I want to pose the question: If we don’t have free will how can anything new be created? And if there was no free will how could you prove something is new? For scientists and engineers they don’t think in philosophy. They are makers. I believe in free will. I don’t see the point of things being predetermined. Of course me not liking a predetermined system does not mean it doesn’t exist.

p = 3 (p^4/((p*Data)^2 + p) ) N[(Data^4/((p*Data)^2 + Data) )] Data = Import["C:\\Users\\Trurl\\Documents\\20220405PrimeTable.csv", "CSV"] These 2 equations are the pattern. N[(Data^4/((p*Data)^2+Data) )] is the pattern to find the smaller factor and (p^4/((p*Data)^2+p) ) is the equation to find the pattern of the error. I post here because I think they were being confused. The start is the first 1000 Primes imported from Wikipedia. Notice 2 is not always considered a Prime number and yields imaginary results. I know I have moved on from this math problem but I thought this post was significant. Looking at the numbers over 1000 instead of 85=5*17. I'll upload the file for download. {{"2", 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71}, {73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173}, {179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281}, {283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409}, {419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541}, {547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659}, {661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809}, {811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941}, {947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069}, {1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223}, {1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373}, {1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511}, {1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657}, {1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811}, {1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987}, {1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129}, {2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287}, {2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423}, {2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617}, {2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741}, {2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903}, {2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079}, {3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257}, {3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413}, {3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571}, {3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727}, {3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907}, {3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057}, {4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231}, {4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409}, {4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583}, {4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751}, {4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937}, {4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087}, {5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279}, {5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443}, {5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639}, {5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791}, {5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939}, {5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133}, {6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301}, {6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473}, {6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673}, {6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833}, {6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997}, {7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207}, {7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411}, {7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561}, {7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723}, {7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919}} p = 3 (p^4/((p*Data)^2 + p) ) 3 {{81/(3 + 9 ("2")^2), 27/28, 27/76, 27/148, 27/364, 27/508, 27/868, 27/ 1084, 27/1588, 27/2524, 27/2884, 27/4108, 27/5044, 27/5548, 27/6628, 27/ 8428, 27/10444, 27/11164, 27/13468, 27/15124}, {27/15988, 27/18724, 27/ 20668, 27/23764, 27/28228, 27/30604, 27/31828, 27/34348, 27/35644, 27/38308, 27/48388, 27/51484, 27/56308, 27/57964, 27/66604, 27/68404, 27/73948, 27/ 79708, 27/83668, 27/89788}, {27/96124, 27/98284, 27/109444, 27/111748, 27/ 116428, 27/118804, 27/133564, 27/149188, 27/154588, 27/157324, 27/162868, 27/171364, 27/174244, 27/189004, 27/198148, 27/207508, 27/217084, 27/220324, 27/230188, 27/236884}, {27/240268, 27/257548, 27/282748, 27/290164, 27/ 293908, 27/301468, 27/328684, 27/340708, 27/361228, 27/365404, 27/373828, 27/386644, 27/404068, 27/417388, 27/430924, 27/440068, 27/453964, 27/472828, 27/482404, 27/501844}, {27/526684, 27/531724, 27/557284, 27/562468, 27/ 578164, 27/588748, 27/604804, 27/626548, 27/637564, 27/643108, 27/654268, 27/688324, 27/711508, 27/723244, 27/747004, 27/759028, 27/777244, 27/814324, 27/820588, 27/878044}, {27/897628, 27/930748, 27/950908, 27/971284, 27/ 978124, 27/998788, 27/1033708, 27/1054948, 27/1076404, 27/1083604, 27/ 1105348, 27/1127308, 27/1142068, 27/1149484, 27/1194484, 27/1232644, 27/ 1240348, 27/1255828, 27/1279228, 27/1302844}, {27/1310764, 27/1358788, 27/ 1374988, 27/1399468, 27/1432444, 27/1474204, 27/1508044, 27/1550884, 27/ 1585588, 27/1611868, 27/1638364, 27/1656148, 27/1692004, 27/1719148, 27/ 1737364, 27/1774084, 27/1792588, 27/1858108, 27/1905628, 27/1963444}, {27/ 1973164, 27/2022124, 27/2031988, 27/2051788, 27/2061724, 27/2111764, 27/ 2182828, 27/2203348, 27/2213644, 27/2234308, 27/2307388, 27/2328484, 27/ 2339068, 27/2360308, 27/2467948, 27/2489764, 27/2533684, 27/2589124, 27/ 2633908, 27/2656444}, {27/2690428, 27/2724628, 27/2805268, 27/2828524, 27/ 2863588, 27/2898868, 27/2946244, 27/2982028, 27/3054244, 27/3078508, 27/ 3115084, 27/3127324, 27/3188884, 27/3201268, 27/3238564, 27/3301204, 27/ 3313804, 27/3377164, 27/3389908, 27/3428284}, {27/3544708, 27/3570844, 27/ 3583948, 27/3610228, 27/3649828, 27/3689644, 27/3743068, 27/3783388, 27/ 3823924, 27/3974404, 27/3988228, 27/4057708, 27/4113724, 27/4184284, 27/ 4226908, 27/4269748, 27/4327204, 27/4414108, 27/4443268, 27/4487188}, {27/ 4531324, 27/4546084, 27/4590508, 27/4680004, 27/4755244, 27/4892188, 27/ 4907524, 27/4938268, 27/4984564, 27/5000044, 27/5046628, 27/5077804, 27/ 5093428, 27/5124748, 27/5219284, 27/5235124, 27/5282788, 27/5556964, 27/ 5606068, 27/5655388}, {27/5721484, 27/5871604, 27/5955844, 27/6074788, 27/ 6108988, 27/6126124, 27/6160468, 27/6212164, 27/6281428, 27/6316204, 27/ 6333628, 27/6386044, 27/6491524, 27/6580084, 27/6597868, 27/6633508, 27/ 6651364, 27/6687148, 27/6741004, 27/6849364}, {27/6958588, 27/7031884, 27/ 7142548, 27/7198204, 27/7235428, 27/7291444, 27/7366468, 27/7404124, 27/ 7479724, 27/7517668, 27/7651228, 27/7689604, 27/7747348, 27/7766644, 27/ 7805308, 27/7863484, 27/7882924, 27/7941388, 27/8039308, 27/8236948}, {27/ 8296708, 27/8336668, 27/8356684, 27/8598748, 27/8639428, 27/8659804, 27/ 8762044, 27/8885524, 27/8906188, 27/9009868, 27/9093244, 27/9156028, 27/ 9219028, 27/9282244, 27/9473188, 27/9537268, 27/9580108, 27/9601564, 27/ 9730804, 27/9839164}, {27/9969988, 27/10057684, 27/10234228, 27/10389964, 27/10457068, 27/10501924, 27/10524388, 27/10569388, 27/10591924, 27/ 10704964, 27/10841404, 27/10909948, 27/10978708, 27/11186284, 27/11209468, 27/11395804, 27/11419204, 27/11678188, 27/11749324, 27/11844508}, {27/ 11916148, 27/11964028, 27/11988004, 27/12036028, 27/12132364, 27/12204868, 27/12326188, 27/12350524, 27/12472564, 27/12644428, 27/12767908, 27/ 12842284, 27/12991684, 27/13016668, 27/13066708, 27/13091764, 27/13217404, 27/13368964, 27/13394308, 27/13597924}, {27/13623484, 27/13700308, 27/ 13751644, 27/13777348, 27/13906228, 27/14009764, 27/14244124, 27/14559628, 27/14612548, 27/14692108, 27/14798524, 27/15012508, 27/15039364, 27/ 15093148, 27/15201004, 27/15417868, 27/15445084, 27/15499588, 27/15608884, 27/15691108}, {27/15773548, 27/15828628, 27/15994444, 27/16022164, 27/ 16328668, 27/16412764, 27/16440844, 27/16525228, 27/16581604, 27/16666348, 27/16864924, 27/16950388, 27/17007484, 27/17036068, 27/17121964, 27/ 17179348, 27/17265604, 27/17438764, 27/17525668, 27/17612788}, {27/17816908, 27/17875444, 27/17963428, 27/18140044, 27/18258268, 27/18347188, 27/ 18406588, 27/18795028, 27/19066324, 27/19217884, 27/19339564, 27/19400548, 27/19492204, 27/19522804, 27/19614748, 27/19953724, 27/20139844, 27/ 20170948, 27/20420644, 27/20546068}, {27/20608924, 27/20798068, 27/21019828, 27/21178948, 27/21210844, 27/21274708, 27/21402724, 27/21498988, 27/ 21595468, 27/21659908, 27/21692164, 27/21756748, 27/21853804, 27/21983548, 27/22048564, 27/22081108, 27/22178884, 27/22342324, 27/22375084, 27/ 22539244}, {27/22671004, 27/22737028, 27/22968868, 27/23135188, 27/23335564, 27/23369044, 27/23469628, 27/23536804, 27/23570428, 27/23840284, 27/ 24077668, 27/24145708, 27/24247948, 27/24384604, 27/24487348, 27/24555964, 27/24865924, 27/25004308, 27/25177828, 27/25282228}, {27/25386844, 27/ 25526668, 27/25701988, 27/25913164, 27/26160628, 27/26231548, 27/26338108, 27/26444884, 27/26480524, 27/26982004, 27/27018004, 27/27198364, 27/ 27343084, 27/27415588, 27/27670108, 27/27743044, 27/27889204, 27/28109164, 27/28219468, 27/28440724}, {27/28514668, 27/28625764, 27/28997644, 27/ 29184484, 27/29221924, 27/29522308, 27/30013708, 27/30089668, 27/30127684, 27/30356284, 27/30470908, 27/30547444, 27/30777628, 27/30893044, 27/ 31047268, 27/31124524, 27/31279324, 27/31707004, 27/31746028, 27/ 31824148}, {27/31863244, 27/32098324, 27/32650204, 27/32689804, 27/32808748, 27/32927908, 27/33047284, 27/33126988, 27/33246724, 27/33286684, 27/ 33526948, 27/33607228, 27/33848644, 27/33888964, 27/34090924, 27/34131388, 27/34455964, 27/34496644, 27/34822948, 27/34945708}, {27/35356468, 27/ 35686804, 27/35852548, 27/35935564, 27/35977108, 27/36060268, 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27/49914724, 27/50208844, 27/ 50257948, 27/50405404, 27/50700964, 27/51096388, 27/51145924, 27/51245068, 27/51393964, 27/51742228, 27/51841948, 27/51891844, 27/52341988, 27/ 52945204, 27/53197564, 27/53349268, 27/53399884, 27/53653324, 27/ 53704084}, {27/53958244, 27/54009148, 27/54264028, 27/54417244, 27/54468364, 27/54724324, 27/54775588, 27/55032268, 27/55186564, 27/55392628, 27/ 56168788, 27/56428708, 27/56480764, 27/56741404, 27/56950348, 27/57107308, 27/57369388, 27/57842644, 27/58000828, 27/58317844}, {27/58635724, 27/ 58688788, 27/59167444, 27/59327428, 27/59434204, 27/59594548, 27/59755108, 27/60238084, 27/60291868, 27/60561148, 27/60939148, 27/61101508, 27/ 61209868, 27/61264084, 27/61372588, 27/62025628, 27/62080204, 27/62408164, 27/62572468, 27/63011668}, {27/63231844, 27/63397228, 27/63562828, 27/ 64060924, 27/64505308, 27/64560964, 27/64672348, 27/64839604, 27/64895404, 27/65062948, 27/65230708, 27/65510788, 27/65679124, 27/66016444, 27/ 66354628, 27/66863524, 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27/ 186141388, 27/186235924, 27/186425068, 27/187277404, 27/187561948, 27/ 188131684}} N[(p^4/((p*Data)^2 + p) )] {{81./(3. + 9. 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1.37293*10^-6, 1.37079*10^-6, 1.36937*10^-6, 1.36652*10^-6, 1.3651*10^-6, 1.36015*10^-6, 1.35804*10^-6}, {1.35664*10^-6, 1.35173*10^-6, 1.34755*10^-6, 1.34616*10^-6, 1.34547*10^-6, 1.33512*10^-6, 1.33375*10^-6, 1.32558*10^-6, 1.32354*10^-6, 1.32152*10^-6, 1.31747*10^-6, 1.31345*10^-6, 1.30878*10^-6, 1.30679*10^-6, 1.30546*10^-6, 1.3048*10^-6, 1.30347*10^-6, 1.29754*10^-6, 1.29557*10^-6, 1.29165*10^-6}} N[(11^4/((11*Data)^2 + 11) )] {{14641./(11. + 121. 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0.0000120487, 0.000011958, 0.000011913, 0.0000118832, 0.0000117943, 0.0000117502, 0.0000116919, 0.0000116628, 0.0000116051, 0.0000114486, 0.0000114345, 0.0000114064}, {0.0000113924, 0.000011309, 0.0000111178, 0.0000111044, 0.0000110641, 0.0000110241, 0.0000109843, 0.0000109578, 0.0000109184, 0.0000109053, 0.0000108271, 0.0000108012, 0.0000107242, 0.0000107115, 0.000010648, 0.0000106354, 0.0000105352, 0.0000105228, 0.0000104242, 0.0000103875}, {0.0000102669, 0.0000101718, 0.0000101248, 0.0000101014, 0.0000100897, 0.0000100665, 0.0000100549, 9.92855*10^-6, 9.8832*10^-6, 9.81575*10^-6, 9.78229*10^-6, 9.7269*10^-6, 9.71588*10^-6, 9.69389*10^-6, 9.66105*10^-6, 9.65014*10^-6, 9.61752*10^-6, 9.56352*10^-6, 9.55277*10^-6, 9.48868*10^-6}, {9.43576*10^-6, 9.42523*10^-6, 9.37283*10^-6, 9.30022*10^-6, 9.26935*10^-6, 9.24886*10^-6, 9.21825*10^-6, 9.17768*10^-6, 9.14742*10^-6, 9.11732*10^-6, 9.03775*10^-6, 8.97876*10^-6, 8.96899*10^-6, 8.94949*10^-6, 8.88172*10^-6, 8.85292*10^-6, 8.83379*10^-6, 8.79573*10^-6, 8.74849*10^-6, 8.71097*10^-6}, {8.68299*10^-6, 8.65515*10^-6, 8.55419*10^-6, 8.52696*10^-6, 8.51791*10^-6, 8.47289*10^-6, 8.41046*10^-6, 8.39275*10^-6, 8.36629*10^-6, 8.28765*10^-6, 8.27898*10^-6, 8.23584*10^-6, 8.176*10^-6, 8.15903*10^-6, 8.15056*10^-6, 8.10841*10^-6, 8.04996*10^-6, 8.03338*10^-6, 8.00036*10^-6, 7.92681*10^-6}, {7.91061*10^-6, 7.88639*10^-6, 7.87834*10^-6, 7.86228*10^-6, 7.83829*10^-6, 7.83032*10^-6, 7.78273*10^-6, 7.76696*10^-6, 7.68884*10^-6, 7.60427*10^-6, 7.55872*10^-6, 7.55117*10^-6, 7.5361*10^-6, 7.51358*10^-6, 7.49116*10^-6, 7.48371*10^-6, 7.46143*10^-6, 7.38057*10^-6, 7.37328*10^-6, 7.35149*10^-6}, {7.29385*10^-6, 7.2724*10^-6, 7.2298*10^-6, 7.22274*10^-6, 7.20161*10^-6, 7.15963*10^-6, 7.10422*10^-6, 7.09734*10^-6, 7.08361*10^-6, 7.06309*10^-6, 7.01555*10^-6, 7.00205*10^-6, 6.99532*10^-6, 6.93516*10^-6, 6.85615*10^-6, 6.82362*10^-6, 6.80422*10^-6, 6.79777*10^-6, 6.76566*10^-6, 6.75926*10^-6}, {6.72742*10^-6, 6.72108*10^-6, 6.68951*10^-6, 6.67068*10^-6, 6.66442*10^-6, 6.63325*10^-6, 6.62704*10^-6, 6.59613*10^-6, 6.57769*10^-6, 6.55322*10^-6, 6.46266*10^-6, 6.4329*10^-6, 6.42697*10^-6, 6.39744*10^-6, 6.37397*10^-6, 6.35645*10^-6, 6.32742*10^-6, 6.27565*10^-6, 6.25853*10^-6, 6.22451*10^-6}, {6.19077*10^-6, 6.18517*10^-6, 6.13513*10^-6, 6.11859*10^-6, 6.10759*10^-6, 6.09116*10^-6, 6.07479*10^-6, 6.02609*10^-6, 6.02071*10^-6, 5.99394*10^-6, 5.95676*10^-6, 5.94093*10^-6, 5.93042*10^-6, 5.92517*10^-6, 5.91469*10^-6, 5.85242*10^-6, 5.84727*10^-6, 5.81655*10^-6, 5.80127*10^-6, 5.76084*10^-6}, {5.74078*10^-6, 5.7258*10^-6, 5.71089*10^-6, 5.66648*10^-6, 5.62744*10^-6, 5.62259*10^-6, 5.61291*10^-6, 5.59843*10^-6, 5.59362*10^-6, 5.57921*10^-6, 5.56486*10^-6, 5.54107*10^-6, 5.52687*10^-6, 5.49863*10^-6, 5.47061*10^-6, 5.42897*10^-6, 5.42437*10^-6, 5.41062*10^-6, 5.40147*10^-6, 5.36062*10^-6}, {5.34262*10^-6, 5.28913*10^-6, 5.2803*10^-6, 5.27589*10^-6, 5.26709*10^-6, 5.25392*10^-6, 5.24955*10^-6, 5.2234*10^-6, 5.21473*10^-6, 5.18455*10^-6, 5.12076*10^-6, 5.09975*10^-6, 5.08721*10^-6, 5.06227*10^-6, 5.0334*10^-6, 5.02111*10^-6, 5.00071*10^-6, 4.9764*10^-6, 4.97237*10^-6, 4.96431*10^-6}, {4.95227*10^-6, 4.93628*10^-6, 4.92433*10^-6, 4.90453*10^-6, 4.90058*10^-6, 4.8927*10^-6, 4.86527*10^-6, 4.85358*10^-6, 4.84194*10^-6, 4.8342*10^-6, 4.82262*10^-6, 4.81877*10^-6, 4.7996*10^-6, 4.79578*10^-6, 4.76537*10^-6, 4.74275*10^-6, 4.72777*10^-6, 4.6943*10^-6, 4.68691*10^-6, 4.67586*10^-6}, {4.65388*10^-6, 4.65023*10^-6, 4.63931*10^-6, 4.62843*10^-6, 4.61759*10^-6, 4.56748*10^-6, 4.55685*10^-6, 4.53219*10^-6, 4.52518*10^-6, 4.51122*10^-6, 4.49384*10^-6, 4.48002*10^-6, 4.4594*10^-6, 4.42874*10^-6, 4.42197*10^-6, 4.41859*10^-6, 4.41184*10^-6, 4.37168*10^-6, 4.35181*10^-6, 4.34192*10^-6}, {4.33863*10^-6, 4.31246*10^-6, 4.30271*10^-6, 4.29299*10^-6, 4.27044*10^-6, 4.25444*10^-6, 4.23219*10^-6, 4.22586*10^-6, 4.17888*10^-6, 4.16957*10^-6, 4.1603*10^-6, 4.15106*10^-6, 4.13878*10^-6, 4.12961*10^-6, 4.12352*10^-6, 4.12047*10^-6, 4.10228*10^-6, 4.09324*10^-6, 4.08722*10^-6, 4.08422*10^-6}, {4.07523*10^-6, 4.04252*10^-6, 4.03367*10^-6, 4.03072*10^-6, 4.02484*10^-6, 3.99855*10^-6, 3.99564*10^-6, 3.98984*10^-6, 3.97251*10^-6, 3.96963*10^-6, 3.96101*10^-6, 3.95529*10^-6, 3.91836*10^-6, 3.90991*10^-6, 3.90149*10^-6, 3.8959*10^-6, 3.88473*10^-6, 3.87085*10^-6, 3.82692*10^-6, 3.80523*10^-6}, {3.80253*10^-6, 3.79446*10^-6, 3.78909*10^-6, 3.78641*10^-6, 3.78106*10^-6, 3.77838*10^-6, 3.76506*10^-6, 3.74654*10^-6, 3.73864*10^-6, 3.73339*10^-6, 3.72292*10^-6, 3.70989*10^-6, 3.70211*10^-6, 3.67634*10^-6, 3.67122*10^-6, 3.66866*10^-6, 3.66101*10^-6, 3.6231*10^-6, 3.61809*10^-6, 3.6081*10^-6}, {3.59567*10^-6, 3.58824*10^-6, 3.58084*10^-6, 3.571*10^-6, 3.56365*10^-6, 3.54902*10^-6, 3.54416*10^-6, 3.53689*10^-6, 3.53448*10^-6, 3.52724*10^-6, 3.52243*10^-6, 3.51523*10^-6, 3.51283*10^-6, 3.50089*10^-6, 3.49851*10^-6, 3.47955*10^-6, 3.47248*10^-6, 3.44907*10^-6, 3.44442*10^-6, 3.43051*10^-6}, {3.41439*10^-6, 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2.80919*10^-6, 2.80406*10^-6, 2.80235*10^-6, 2.79724*10^-6, 2.79384*10^-6, 2.77862*10^-6, 2.77189*10^-6, 2.76185*10^-6, 2.74689*10^-6, 2.7337*10^-6, 2.72877*10^-6, 2.72713*10^-6, 2.71733*10^-6}, {2.71245*10^-6, 2.70435*10^-6, 2.70273*10^-6, 2.69467*10^-6, 2.69307*10^-6, 2.68825*10^-6, 2.68025*10^-6, 2.66912*10^-6, 2.66595*10^-6, 2.64706*10^-6, 2.64549*10^-6, 2.63302*10^-6, 2.63147*10^-6, 2.62372*10^-6, 2.62218*10^-6, 2.61447*10^-6, 2.59917*10^-6, 2.59612*10^-6, 2.5946*10^-6, 2.59157*10^-6}, {2.58551*10^-6, 2.57346*10^-6, 2.56896*10^-6, 2.56447*10^-6, 2.56298*10^-6, 2.55405*10^-6, 2.54222*10^-6, 2.53633*10^-6, 2.5334*10^-6, 2.52901*10^-6, 2.50721*10^-6, 2.50577*10^-6, 2.49857*10^-6, 2.49714*10^-6, 2.49284*10^-6, 2.48998*10^-6, 2.4857*10^-6, 2.48143*10^-6, 2.47575*10^-6, 2.47151*10^-6}, {2.46868*10^-6, 2.46024*10^-6, 2.45604*10^-6, 2.45045*10^-6, 2.4421*10^-6, 2.43933*10^-6, 2.42966*10^-6, 2.42142*10^-6, 2.41458*10^-6, 2.39829*10^-6, 2.39424*10^-6, 2.38618*10^-6, 2.38217*10^-6, 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2.02868*10^-6}, {2.02658*10^-6, 2.01926*10^-6, 2.01301*10^-6, 2.01093*10^-6, 2.0099*10^-6, 1.99444*10^-6, 1.9924*10^-6, 1.98018*10^-6, 1.97715*10^-6, 1.97412*10^-6, 1.96808*10^-6, 1.96207*10^-6, 1.95509*10^-6, 1.95211*10^-6, 1.95013*10^-6, 1.94914*10^-6, 1.94716*10^-6, 1.9383*10^-6, 1.93536*10^-6, 1.9295*10^-6}} In[14]:= N[(Data^4/((p*Data)^2 + Data) )] Out[14]= {{("2")^4/("2" + 9. 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@Sensei and others. You know more about the tech aspects than me. I am 20 years behind. I am behind on making modern websites. But that is a future thread. How big is a current jpeg pic? 12 megs? When I was in graphics school web stuff for the computer screen we keep it 72mp. For print it would be increased. We were taught that RGB and CMYK were just different color scales and you change them to match print colors to the desired screen colors. Like how the paint of the car looks different under fluorescent light. I also do not know how the print head mixes colors. And how it breaks the resolution of the pic to colors. But that is complex. It has been perfected over 40 years. I have some graphic experience. Some of the best graphics I have seen is simple black and white. Back in the 80’s people made zines and comics on a black and white photocopiers. One time I had a $5000 color copier that was useless because we didn’t have a $7000 computer interface. I tell this story just to illustrate sometimes the inkjet is overkill for print graphs let alone expensive. More the art side then the science. But we are supposed to fit the science to meet the needs of the art. What type of art is everyone making? I know this is a science forum but STEAM (science, technology, engineering, art, and math).

For the pixels on your computer screen the primary colors of red, blue, and green are arbitrary. It is just a reference. You have white 255, 255, 255 as a mixture of all colors and black 0,0,0. All other colors are a variation of that scale. That is a light source. For printing a different primary scale is used. I don’t know why they picked CMYK. It is just a stating point. I don’t believe you mix these colors like paint. Because as you know from Kindergarten it makes different shades of brown. I was taught that print work is also pixelated like the grays of a news paper. Gray is black pixels spaced further apart. I am still confused when Photoshop ask which primary colors you want to use. I don’t print much work. But you will see the color scheme in the properties.

You are probably wondering why I replied to your post a year after you wrote it. I did not see this post. I am posting a second time to ask if your scientific computation has led you to mine bitcoin. The reason I ask is that I want to study bitcoin and the blockchain. Many participants to this forum community sigh when I talk about breaking RSA. But to break RSA you have to factor a large semi-Prime. I attempted to find a pattern in the factorization of factors and not a pattern in Primes. If you can factor the semi-Prime you can break RSA. But most public key crypto relies on finding Primes. Bitcoin relies on elliptic curve crytpo, But it too relies on the modulus and a large Prime number. The elliptic curve crypto creates a public and private key that control the redemption of bitcoin. Imagine if we could find these Prime numbers we could take any public key on the blockchain and collect as many coins as we wanted. There have been new stories of crypto currency theft, but the problem is not collecting the coins but liquifying them as cash. The block chain protects theft by record of transactions. I am not suggesting we steal bitcoin. I am just saying bitcoin is not secure. I do not understand the technical details of elliptic crypto, but in my reading it mentioned and attack based on large Prime numbers. I know everyone is mining crypto, but it still might be a field of data science you wish to explore. I am just starting to study it. Perhaps it would be better to mine crypto legally. I posted my “Simple Yet Interesting” thread looking for collaboration in solving public key crypto, I am not naive. I understand why no one takes the post seriously. But I tell you that you will not find a pattern in Primes until you find a pattern in factoring. I intend to use data science to show my equations. Again, the problem to defeat public key crypto is not just a pattern in Primes. Almost all of the one-way-functions rely on factoring. To me this is the biggest flaw in public key crypto. To explain what I mean, if a factor has only 2 numbers other than 1 and itself you can estimate where the factors occur. If the first factor is small the other factor is large. If the second factor is large only certain smaller numbers can be multiplied to get a result. Yes, this is difficult and time consuming if you set your rules correctly you have limited estimates. This is well known, I claimed, for the special case where only 2 Prime factors exist. The rules can be put into an equation and find the factors due to the fact that there are only 2 factors. So in conclusion, that is my data science project. I want to study bitcoin. But I fear one day block chains will crash once the ciphers they are based on are defeated. The whole crypto currency seems very much like an elegant scheme. But what if the computer data can’t find any pattern? The pattern is there, we just can’t see it. We are looking for series or higher mathematics when a simple solution is best.

I too am interested in scientific computing. I have a degree but there is a ton of stuff I don’t know. Do you mean science problems or data science? The web is full of science problems but finding resources for data science seems more difficult. I want to crunch primes or test multiple patterns in numbers. Some stuff Wolfram Alpha helps. But I want more control like in a programming language. I know Mathematica and Excel and Python can help. But there is also a problem of finding data unless you are creating your own. YouTube should have some stuff but I haven’t found a good video on number crunching. So if any knows how to program a program for recursion or factions let me know. Where you thinking mining crypto?

Looks like a protractor to me. It is going from 0 to 90. It does have many scales but it just looks like it is made for a map. There are many things it would be able to do on a map. Like taking the scale on the map versus actual distance. That is my guess. What other pictures did the search engine show that were similar?

This is just first inspection. But a kind of intuition starting point. Thus it probably doesn't work. But I just needed a starting point to test where I think zeros could occur. And where if they didn't occur would show. I believe zeros could only occur with even numbered fractions. But then again what do I know. In memory of Pappy Craylar: Hypothesis on critical zeros on Riemann Zeta Function Non-critical zeros have been found at an x-value of ½ Possibly forming an isosceles triangle. What if we were to expand this to all even powers. That is ½ , ¼ , ⅙ … towards zero and ½ + ½^(½^n)... towards 1? This fraction combined with and complex number would alternate between positive and negative values cancelling out to form zero. First we should test values at ¼ that are a similar isosceles triangle to ½ non-trivial zeros. If we can not find a trivial zero at these values it supports the Riemann Hypothesis.

http://www.dtc.umn.edu/~odlyzko/zeta_tables/index.html https://mathworld.wolfram.com/RiemannZetaFunctionZeros.html https://m.youtube.com/watch?v=sD0NjbwqlYw&pp=QAFIAQ%3D%3D https://m.youtube.com/watch?v=d6c6uIyieoo These are the best explanations I have found so far. It is enough to get started. I still don’t understand the displacement of Prime numbers as it relates to the zeta function. My attempts in my post “Simple Yet Interesting” I encountered complex numbers and I also had decimals and fractions. I am looking back here the Riemann Zeta function also deals with those. So I’m wondering why a was searching for a perfect integer. I have some trials I want to test for zeros. The complex numbers are a game changer. Well I moved on to a new problem. Unfortunately it too is related to Prime numbers. Proving it wrong I would need to find a nontrivial zero. I don’t have a clue how to prove it is always true. If that is even possible. My goal is to learn and perform my own zeros tests.

Can no one explain the distribution of Primes according to the Riemann hypothesis? All that I have seen or read is that the importance of the Riemann hypothesis is the distribution of Primes, but no one explains why it works. This is different from my last project. The reason I want to know is the same though. Is it a correct statement that: *the Prime Factorization problem (RSA) *the discrete logarithmic problem *elliptic curve cryptography All rely on factorization and Prime distribution? My goal is to start a different math project. I just want to find zeros and start with zeros that already exist. In my post “Simple Yet Interesting” someone asked why I was factoring semi-Primes to hopefully solve RSA. As most of you know, that is the basis of RSA’s one-way-function. That was what the cipher was based. All I tried to do was take the semi-Prime and see why it couldn’t be factored. I want to take the simplest concept of the Riemann hypothesis and see why it is I cannot find a zero. I am going to attach a paper I wrote 11 years ago. It was a simple outline. My instructor corrected grammar and citation format. I argue that it is a good outline of cryptography for only having to be a 3 page paper. Let me know what you think. Is it that bad? I get frustrated when I research something and the comments the instructor leaves on my paper is, “the comma comes after the parenthesis.” Is the paper a good description of how cryptography evolved? TrurlCryptoSurveySFN002.docx

Can anyone explain in one paragraph or equation how the Riemann hypothesis implies a pattern in Prime numbers? The hypothesis an easy enough to follow the problem, but the pattern in Primes is not clear to me. I’m sure a Google search may be helpful, but I wanted to work it through on my own. I find it helpful to take one small part if the problem and see what it does. Take the book Practical Cryptography. It explains all the ciphers. They are all open source. Doesn’t mean you can solve them but it lets you see the inner workings. That is what I need an explanation of the patterns in Primes in the Riemann hypothesis. I hope you understand why I just don’t google it. I want to search for nontrivial zeros. And I want to keep it simple.

I was watching a lecture series on science and religion. The instructor mentioned the Conflict Model. In this model religion and science are in conflict. Evolution vs Creationism. Observation vs. History. But the instructor said these polar opposites were once part of the same reasoning. Before the 19th Century, science and religion were often related. I don’t care what you believe. I am a person and have my own views. I just think people are being influenced a bad way. Instead of respecting each other and different views, we are trying to impose our views on others. Not that that is always wrong, but look at the government. Democrats can agree with Republicans. People can’t agree on masks and so forth. What would be the advantage of so much hostile division? I don’t know. I hypothesis it is a way to justify wars. In my speculation it is like: kill and displace millions then leave a mess and say it was too expensive. In this speculation, it is not clear what the true mission is. I will leave with a thought on a video game. In Metal Gear Solid 4 you spend 15 hours fighting Liquid (the name of the opposing enemy). And it turns out that Liquid actually saved the world. So you are the bad guy. I know some of you won’t know the classic game reference, but if you do it is a good topic of discussion.

So all three ways are equal? You are right all 3 should be explained so you know what the equation is doing. Did the instructor plug and chug or was it derived? Obviously the equation is easier. I think the instructor’s goal was to find the frequency and create an equation that could be reused. My question is if you graph the sine wave and take the angle between those points, how are you sure the drawn sine wave is the same as the equation wave? I mean did you form a curve that is equal value for value of the equation and do all points align? Would you have to make new “measurements” for each point to “shape” the modified sine wave to the actual modified sine wave? I said the equation was easier. I meant easier once you know what is what. If I was in that class I would be confused too. But that is why I am asking questions. I never took physics 102 and I know how important this is too electricity and radio waves.

Klapaucius, uh um, I mean Ghideon, You act as there is noting of value in this tread. Sure, breaking RSA would be quite a feat. But you must admit there is no other method that does it. There is no guarantee the Pappy Craylar Method works. And I have moved on to other projects. However, we had an active discussion that may lead to something that might find a different approach. You see, The Pappy Craylar Method is based on the fact that if you increase the size of one factor you must decrease the other. And since there is only one way the Semi-Prime factors go together, the equation to find the factors eliminates possibilities. Sure, the number of possibilities isn’t only one and sometimes the possibilities are further or closer to zero. But until a solution exists, the method leads to the ability to guess the factors by trial and error. See my construction of the 2 graphs that intersect at 5. Of course, I already new the answer, but don’t you find the PC method simple yet interesting? In[89]:= pnp = 85 x = 5 Show[{Plot[(x^4/(pnp^2 + x)), {x, 0, 10}], Plot[(pnp - (x*Sqrt[(pnp^3/(pnp* x^2 + x))])), {x, 0, 10}]}] Out[89]= 85 Out[90]= 5 In[109]:= Clear[pnp, x] pnp = 8637 {Plot[(x^4/(pnp^2 + x)), {x, 0, 3}] Plot[(pnp - (x*Sqrt[(pnp^3/(pnp* x^2 + x))])), {x, 0, 3}]} Out[110]= 8637 Does this work for every Semi-Prime? Maybe, maybe not. This is all I have to share. I am moving on to other projects. So, unless some idea comes along, I will not post. Is my last message Simple, yet interesting?

You must tell me why RSA is not affected by this thread. We can agree that RSA was based on the Prime factorization problem. That is factoring Semi-Primes into the Prime factors. So you must not trust my algebraic equations that estimate where the factors of semi-Primes occur. That is the basis of my work. I think I have stated what they do. But in your test where N=p*q where do you not believe p cannot be found knowing only N? \(q\sqrt {\frac {\text {pnp}^3} {\text {pnp} q^2 + q}}\)

@Ghideon I know you are not going to like my explanation, but q/N is enough to get an estimate of N. Yes I know it is true for all numbers, but using the reciprocal of p and q helps determine where they are positioned on the number line. For semi-Primes my hypothesis is that q/N will reduce to 1/p. Then take 1/p and multiply it by N. You could argue that it is no more useful than recursive division. However, it does give an estimate of where y lies on the number line. And it could further improve estimates of x when determining how far (N minus p) is from (N minus p calculation). I know it seems dumb. Why did we divide in the first place if a simple q/N could solve the solution? And it is a high possibility it doesn’t work. But I am saying the simple solution to the semi-Prime factors problem is helpful. That is: not helpful for a beautiful math equation, but helpful when trying to find a hack to defeat a problem that was never a one-way-function from the start. Clear[pnp, q] pnp = 85 q = 17 Simplify[(q^2 - (pnp*q^2 + q)/ pnp)] Out[139]= 85 Out[140]= 17 -(1/5) ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ \ ___ ___ ___ ___ ___ ___ __ In[142]:= Clear[pnp, q] pnp = 85 q = 19 Simplify[(q^2 - (pnp*q^2 + q)/ pnp)] Out[143]= 85 Out[144]= 19 -(19/85) ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ \ ___ ___ ___ ___ ___ ___ ___ In[146]:= Clear[pnp, q] pnp = 293*3 q = 293 Simplify[(q^2 - (pnp*q^2 + q)/ pnp)] Out[147]= 879 Out[148]= 293 Out[149]= -(1/3) ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ \ ___ ___ ___ ___ ___ ___ ___ _ In[150]:= Clear[pnp, q] pnp = 293*3 q = 291 Simplify[(q^2 - (pnp*q^2 + q)/ pnp)] Out[151]= 879 Out[152]= 291 Out[153]= -(97/293) In[154]:= N[-(97/293)] In[155]:= -0.3310580204778157`* 293*3 Out[155]= -291.

Why? Because it is p^2 minus p^2 derived. Same with second equation. It is just how I derived the equations. Does it work? I don’t know. But I am simply comparing patterns in division. Obviously you tried test values. Did it work with your values? i will run more test values. Let me know if you have any more questions or your test values don’t work.