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 Showing results 1 to 25 of 28 Search took 0.01 seconds. Search: Posts Made By: NHoodMath
 Forum: Miscellaneous Math 2021-02-07, 15:55 Replies: 17 Views: 1,438 Posted By NHoodMath Other closed form of the Hugo sequence and observations There is a much simpler closed form for the Hugo Numbers than what has been posted by Hugo and the others, they are equal to: (Sum from k=0 to k=(p-1)/2 of (Binomial(p, 2*k)*13^k))/2^(n-1) It...
 Forum: Conjectures 'R Us 2021-01-07, 22:44 Replies: 132 Views: 35,269 Posted By NHoodMath I already had this one (R2021) searched to 13K,... I already had this one (R2021) searched to 13K, going to 25K rn (BTW I did finish those 3 k's on S2020 to n=100K, no primes)
 Forum: enzocreti 2020-02-17, 22:17 Replies: 7 Views: 1,136 Posted By NHoodMath Certainly a low-weight sequence, but... Certainly a low-weight sequence, but 5*(10^156-1)/9+360268786 is prime.
 Forum: enzocreti 2020-02-13, 22:30 Replies: 3 Views: 1,183 Posted By NHoodMath There is a mathematically rigorous way to analyze... There is a mathematically rigorous way to analyze this. Repunit numbers can also be written as numbers of the form (10^n-1)/9, with n a positive integer. (10^21-1)/9 is the smallest repunit...
 Forum: enzocreti 2020-02-13, 22:18 Replies: 6 Views: 879 Posted By NHoodMath x^3-y^3=(x-y)(x^2+xy+y^2), so if x-y=1, then... x^3-y^3=(x-y)(x^2+xy+y^2), so if x-y=1, then y=x-1 and the quadratic becomes x^2+x(x+-1)+(x-1)^2=x^2+x^2-x+x^2-2x+1=3x^2-3x+1, so if 3x^2-3x+1 is a Mersenne prime, then x^3-y^3 is also a Mersenne...
 Forum: enzocreti 2020-02-13, 21:55 Replies: 6 Views: 879 Posted By NHoodMath x^3+y^3=(x+y)(x^2-xy+y^2), so yes there are... x^3+y^3=(x+y)(x^2-xy+y^2), so yes there are infinitely many numbers x and y such that x+y is divisible by 43, and thus x^3+y^3 as well by association.
 Forum: enzocreti 2020-02-10, 23:39 Replies: 3 Views: 1,030 Posted By NHoodMath Enzo, here is some relevant maths to what you... Enzo, here is some relevant maths to what you have posted here: The number 51, in your case, you were testing to see whether it was a quadratic residue (mod 163), that is, whether or not there is...
 Forum: Conjectures 'R Us 2020-02-06, 03:17 Replies: 40 Views: 17,811 Posted By NHoodMath Just as a note so if dannyridel is interested,... Just as a note so if dannyridel is interested, use covering.exe for small CK (say k<2^32) and bigcovering.exe for larger CK than 2^32. There is a bug in the covering.exe program for k's greater than...
 Forum: Conjectures 'R Us 2020-02-05, 22:51 Replies: 40 Views: 17,811 Posted By NHoodMath Sweety's code appears to be brute-forcing the CK... Sweety's code appears to be brute-forcing the CK search. Doing it rigorously requires advanced mathematics (modulo arithmetic, orders mod n, Chinese Remainder Theorem, sometimes quadratic, cubic...
 Forum: Conjectures 'R Us 2020-02-02, 23:38 Replies: 3,857 Views: 289,239 Posted By NHoodMath Just making sure you are aware that k values... Just making sure you are aware that k values 2704, 61009, and 786615 can be eliminated from the conjecture, 2704 due to 52^2 and 541 on odd n, 786615 due to 15*229^2 and 541 on even n, and 61009 due...
 Forum: Conjectures 'R Us 2020-02-01, 15:53 Replies: 132 Views: 35,269 Posted By NHoodMath Sierp base 2020 complete to 25K. 21 k's at 10K -... Sierp base 2020 complete to 25K. 21 k's at 10K - 6 k's found prime for 10K-25K = 15 k's remaining. Base released except k=12, 402, and 892. K's remaining: 12 138 255 259 291 390 402 430 471
 Forum: Conjectures 'R Us 2020-01-31, 23:54 Replies: 3,857 Views: 289,239 Posted By NHoodMath If you are using LLR, remove k's from testing by... If you are using LLR, remove k's from testing by manually adding ks(k-value)=1 to llr.ini (ex ks1968=1 for k=1968 removal)
 Forum: Conjectures 'R Us 2020-01-24, 23:11 Replies: 132 Views: 35,269 Posted By NHoodMath next prp 189*2020^20878+1 363*2020^22046+1
 Forum: Conjectures 'R Us 2020-01-19, 19:08 Replies: 132 Views: 35,269 Posted By NHoodMath sweety, CRUS does not intend any work on k's > CK... sweety, CRUS does not intend any work on k's > CK because the project's goal is simply to solve the 1st conjecture for each individual base. If k's > CK were included, decisions would have to be made...
 Forum: Conjectures 'R Us 2020-01-18, 22:48 Replies: 132 Views: 35,269 Posted By NHoodMath @sweety, R2048 has 2 k remaining, k=5 and k=11,... @sweety, R2048 has 2 k remaining, k=5 and k=11, both searched to very high limits over n=4M base 2 after accounting for the Riesel Sieve effort. Most other bases on your list have more k's remaining,...
 Forum: Conjectures 'R Us 2020-01-06, 22:19 Replies: 132 Views: 35,269 Posted By NHoodMath next PRP 411*2020^14877+1 tested to 17.8K, 17... next PRP 411*2020^14877+1 tested to 17.8K, 17 k's remain. I expect this to be done within the week
 Forum: Conjectures 'R Us 2020-01-03, 18:36 Replies: 3,857 Views: 289,239 Posted By NHoodMath 624=16*39 624=4^2*39 Any k that is a square... 624=16*39 624=4^2*39 Any k that is a square times the leftover non-square part of the base (39) has algebraic factors for odd n. These sometimes combine with a trivial factor (in this case 5) to...
 Forum: Conjectures 'R Us 2020-01-01, 14:33 Replies: 132 Views: 35,269 Posted By NHoodMath I think base 2019 and 2017 were the most... I think base 2019 and 2017 were the most thoroughly searched of the "year" bases. Lalera did his hard work on getting the Riesel side of 2019 to n=200K (!) and the Sierp side, if not already tested...
 Forum: Conjectures 'R Us 2020-01-01, 06:28 Replies: 132 Views: 35,269 Posted By NHoodMath Comparing k's remaining w/VBCurtis Just to check if we have the same 59 k's remaining: 9, 32, 42, 99, 128, 156, 171, 207, 216, 261, 275, 317, 345, 419, 428, 429, 471, 473, 519, 563, 582, 657, 687, 704, 776, 786, 788, 872, 941, 1023,...
 Forum: Conjectures 'R Us 2020-01-01, 06:17 Replies: 132 Views: 35,269 Posted By NHoodMath You can go ahead and test 10K-25K or however far... You can go ahead and test 10K-25K or however far you wish. I honestly want no more part in that base
 Forum: Conjectures 'R Us 2019-12-31, 15:00 Replies: 132 Views: 35,269 Posted By NHoodMath Find attached the 6915 candidate sequences for... Find attached the 6915 candidate sequences for R2020 8K=10K to n=5G (102.2s/n) Also, status update on yesterday's S2020 reservation: Testing is at n=14676, 3 new primes found, 18 k's remain:...
 Forum: Conjectures 'R Us 2019-12-31, 00:51 Replies: 132 Views: 35,269 Posted By NHoodMath How long does a test of a 20000 digit long number... How long does a test of a 20000 digit long number take on your computer @VBCurtis? That way I can judge optimal depth
 Forum: Conjectures 'R Us 2019-12-30, 20:45 Replies: 132 Views: 35,269 Posted By NHoodMath Reserving Sierp. base 2020 (all 21 k's) from... Reserving Sierp. base 2020 (all 21 k's) from 10K-20K. (At 10K the testing was progressing at about n=1K/day) also, just ask if you want the k's remaining at n=10K for this one. Anyone want all 62...
 Forum: Conjectures 'R Us 2017-08-18, 22:14 Replies: 2,281 Views: 198,372 Posted By NHoodMath R411 I am taking the whole base, Bitcoin.
 Forum: Conjectures 'R Us 2017-08-18, 20:54 Replies: 2,281 Views: 198,372 Posted By NHoodMath R411 I have started work on Riesel base 411, CK 60254. So far, I have tested K<15K to 2.5K and will post weekly updates as I progress toward 25K.
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