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 Showing results 1 to 25 of 1000 Search took 0.16 seconds. Search: Posts Made By: R. Gerbicz
 Forum: Math 2021-04-13, 15:59 Replies: 6 Views: 4,554 Posted By R. Gerbicz You need a greater precision, roughly 16 digits... You need a greater precision, roughly 16 digits to get the correct answer for all p<10^8. Real example using Pari-Gp: ? n=181605302766736484827; ? \p realprecision = 38 significant digits ? ...
 Forum: Math 2021-04-13, 12:58 Replies: 4 Views: 138 Posted By R. Gerbicz I've written a quite different formula. At least... I've written a quite different formula. At least one PRP/LL test has performed on each prime for p<10^8. Lets check out what your original formula says about the number of Mersenne primes for p in...
 Forum: Math 2021-04-12, 23:09 Replies: 4 Views: 138 Posted By R. Gerbicz Your error is in the assumptation that mp is... Your error is in the assumptation that mp is prime by 1/log(mp) probability. The true is that it is prime by a "much" larger probability: c*log(log(mp))/log(mp) probability [what is...
 Forum: Prime Gap Searches 2021-04-05, 13:51 Replies: 18 Views: 518 Posted By R. Gerbicz For that record used only your 1st method with... For that record used only your 1st method with the following modification: collect in array/vector those res values that occur maximal times as x%p and choose randomly(!) one res value from these....
 Forum: Prime Gap Searches 2021-04-02, 23:22 Replies: 18 Views: 518 Posted By R. Gerbicz Improved solution with 6727 numbers survived the... Improved solution with 6727 numbers survived the sieve: ...
 Forum: YAFU 2021-03-24, 22:48 Replies: 62 Views: 27,757 Posted By R. Gerbicz Found these two posts from different threads: ... Found these two posts from different threads: https://www.mersenneforum.org/showpost.php?p=54147&postcount=33 https://www.mersenneforum.org/showpost.php?p=530352&postcount=23
 Forum: PrimeNet 2021-03-22, 23:06 Replies: 8 Views: 368 Posted By R. Gerbicz These were discussed multiple times. A new thing... These were discussed multiple times. A new thing to demonstrate that the shiftcount trick is actually not enough! We claim that mult(x,y,p) returns (x*y)%(2^p-1), and implement [correctly!] the...
 Forum: Hardware 2021-03-21, 17:00 Replies: 16 Views: 732 Posted By R. Gerbicz Checkout that p95 can change the blocksize, I... Checkout that p95 can change the blocksize, I don't see any advantage to fix it. Yes, that is true. I have overlooked that as I can remember gpuowl is a little tricky in this area, because it...
 Forum: Hardware 2021-03-21, 12:13 Replies: 16 Views: 732 Posted By R. Gerbicz Looks like my above formula is good, my... Looks like my above formula is good, my reasoning: we have q=(1-e)^B probability that in a single block all B iterations is good. You have 2*sqrt(B) iterations to do the in the check per block, and...
 Forum: Hardware 2021-03-19, 21:07 Replies: 16 Views: 732 Posted By R. Gerbicz Suboptimal run, with those many errors you could... Suboptimal run, with those many errors you could get a very good approx for the error rate and using that you/we could optimize the block size to lower the expected number of iterations. Check me:...
 2021-03-11, 17:14 Replies: 27 Views: 812 Posted By R. Gerbicz It is a perfect counterexample to your claim in... It is a perfect counterexample to your claim in the first post. Likely a=11 seems to be equally good just as a=3, maybe there is no other counterexample for a=11. Let me check [only the first few odd...
 2021-03-11, 16:16 Replies: 27 Views: 812 Posted By R. Gerbicz So you want to say that if a^((mp-1)/2)==-1 mod... So you want to say that if a^((mp-1)/2)==-1 mod mp for given a>2 then mp is prime. It would follow that Mp is always prime(!), just use a=-1+mp. To see a non-trivial counterexample: let a=11 and...
 Forum: Miscellaneous Math 2021-03-04, 18:03 Replies: 15 Views: 599 Posted By R. Gerbicz Destroyed? rate=0.1;year=21;(1+rate)^year ... Destroyed? rate=0.1;year=21;(1+rate)^year rate=0.03;year=3;(1-(1+rate)^(-year))/rate answer: %1 = 7.4002499442581601012110000000000000000 %2 = 2.8286113548946809221333416306177114687
 Forum: Factoring 2021-03-03, 15:21 Replies: 13 Views: 2,333 Posted By R. Gerbicz An early slide from him:... An early slide from him: https://eurocrypt2009rump.cr.yp.to/e074d37e10ad1ad227200ea7ba36cf73.pdf Forums about these claims:...
 Forum: Miscellaneous Math 2021-03-02, 20:32 Replies: 7 Views: 507 Posted By R. Gerbicz Very standard heuristic idea gives that we are... Very standard heuristic idea gives that we are expecting very few [maybe zero] composites for G=nextprime(n!)-n! [if we exclude the G<2 cases]. As you noted to find composite G we need G>n^2 so...
 Forum: Data 2021-02-24, 20:17 Replies: 558 Views: 83,035 Posted By R. Gerbicz We had already a Prp-cf test on this: ... We had already a Prp-cf test on this: https://www.mersenne.org/report_exponent/?exp_lo=82939&exp_hi=&full=1 Notice that for N=(k*2^n+c)/d we're using a Fermat test using base^d as base, then...
 Forum: Miscellaneous Math 2021-02-20, 09:53 Replies: 4 Views: 294 Posted By R. Gerbicz Repeated digit sum has a name:... Repeated digit sum has a name: https://en.wikipedia.org/wiki/Digital_root .
 Forum: Miscellaneous Math 2021-02-19, 20:18 Replies: 32 Views: 1,686 Posted By R. Gerbicz Nice. You can negate that: x=F(n-1)/(F(n-2)-1)... Nice. You can negate that: x=F(n-1)/(F(n-2)-1) mod F(n) And in general: if n=u^4+1 then for x=(u^2+1)/u: x^2==2 mod n.
 Forum: Miscellaneous Math 2021-02-19, 15:18 Replies: 32 Views: 1,686 Posted By R. Gerbicz Yes, that was my method. Yes, that was my method.
 Forum: Miscellaneous Math 2021-02-19, 10:36 Replies: 32 Views: 1,686 Posted By R. Gerbicz And with linear algebra would you need... And with linear algebra would you need primepi(100)+eps=25+eps relations ? OK, take my challenge factor my GRSA100 [G means Gerbicz], n=p*q number with 100 digits. You can use "your" method, and...
 Forum: Miscellaneous Math 2021-02-19, 08:22 Replies: 32 Views: 1,686 Posted By R. Gerbicz Yes, used those known factors, but how? I mean if... Yes, used those known factors, but how? I mean if M|N then we know only small squared residues mod M in the range of sqrt(M), but we need these residues mod N and not mod M. Ofcourse you can regard...
 Forum: Miscellaneous Math 2021-02-19, 01:00 Replies: 32 Views: 1,686 Posted By R. Gerbicz Actually it is easy, using the OP's other... Actually it is easy, using the OP's other favourite number: F12 Fermat number [which was unfactored yesterday]: N=2^4096+1;...
 Forum: Information & Answers 2021-02-15, 17:10 Replies: 26 Views: 6,983 Posted By R. Gerbicz Oh, yes that is even better what I've written,... Oh, yes that is even better what I've written, and maybe: forcing that the server wouldn't give out the same prime exponent twice per day. In this way even if you have a fully factorized mp you would...
 Forum: Information & Answers 2021-02-14, 23:39 Replies: 26 Views: 6,983 Posted By R. Gerbicz Interesting topic. Still don't see a way, my... Interesting topic. Still don't see a way, my failed approach in the prp(!) setup: The key idea is to change the base after a successful mining to a random base with say 64 bits. And then the new...
 Forum: Homework Help 2021-02-13, 21:46 Replies: 3 Views: 490 Posted By R. Gerbicz If x is composite then we know: ... If x is composite then we know: c*x/log(log(x))0 is a constant [c=0.25 is good for all x>6]. ok, not very elegant to use these, though this is still elementary. With...
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