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 Showing results 1 to 25 of 1000 Search took 0.25 seconds. Search: Posts Made By: R. Gerbicz
 Forum: Homework Help 2021-11-27, 16:10 Replies: 23 Views: 4,017 Posted By R. Gerbicz Modified your idea, close to a pure combinatorial... Modified your idea, close to a pure combinatorial proof: The k=0 case is trivial, so assume that 0
 Forum: Wagstaff PRP Search 2021-11-26, 21:04 Replies: 7 Views: 464 Posted By R. Gerbicz Wagstaff numbers are pretty special cyclotomic... Wagstaff numbers are pretty special cyclotomic numbers, these are polcyclo(2*p,2)=(2^p+1)/3. There is no known fast tests (at speed of LL test), though there could be! Note that here for example...
 Forum: Homework Help 2021-11-26, 19:49 Replies: 23 Views: 4,017 Posted By R. Gerbicz I see where you could use Wilson theorem in the... I see where you could use Wilson theorem in the problem, though those solutions would be a little ugly. But really don't see what is in the next chapter and what you could/should use. Freely use...
 Forum: Programming 2021-11-25, 21:08 Replies: 4 Views: 266 Posted By R. Gerbicz Up to constant factor it should be the same... Up to constant factor it should be the same speed. Then analyse how much memory your code needs. Also if you'd contruct all integers in that way then your code runs in quadratic time and needs much...
 Forum: Programming 2021-11-25, 19:03 Replies: 4 Views: 266 Posted By R. Gerbicz You need only mpz_setbit(), this is optimal in... You need only mpz_setbit(), this is optimal in speed/complexity, (you set the ones in the expansion). For example this runs in 0 second: (maybe you should build up from the other direction,...
 Forum: Wagstaff PRP Search 2021-11-25, 18:41 Replies: 7 Views: 464 Posted By R. Gerbicz It will become a viable test when you prove that... It will become a viable test when you prove that it generates all Wagstaff primes, and gives no composites. Until that it is "only" a claim. Thanks:)
 2021-11-23, 15:03 Replies: 14 Views: 581 Posted By R. Gerbicz Here it is that free article:... Here it is that free article: https://www.ams.org/journals/mcom/1989-52-185/S0025-5718-1989-0946602-9/S0025-5718-1989-0946602-9.pdf You want to use theorem 6, then check it again, what they write,...
 2021-11-22, 20:42 Replies: 14 Views: 581 Posted By R. Gerbicz We use different letters, but never mind. For... We use different letters, but never mind. For q=3 (p=7) your test fails, otherwise it is good up to at least q=1000. I don't know how it could be good with correct proof after q=3 (not checked the...
 Forum: Math 2021-11-22, 15:15 Replies: 9 Views: 253 Posted By R. Gerbicz Yes, it is pure luck, basically you have... Yes, it is pure luck, basically you have something 1/(B1*log(B1)) probability to see this lucky find (in this calc we don't assume that there is exactly one prime factor>B1). Another type of...
 Forum: Math 2021-11-22, 14:26 Replies: 9 Views: 253 Posted By R. Gerbicz The OP's question is still valid, you can really... The OP's question is still valid, you can really find a factor for that p-1 is not smooth, beyond the B1 limit (with ofcourse excluding here the special factors for special numbers). Example: use...
 Forum: Math 2021-11-21, 16:55 Replies: 4 Views: 265 Posted By R. Gerbicz Yes, and with that oldish certificates you would... Yes, and with that oldish certificates you would only double check the first computation, what Gimps has done in the past. Then call the new method as fast certificate, because you need there roughly...
 Forum: Math 2021-11-21, 13:32 Replies: 4 Views: 265 Posted By R. Gerbicz OP wants something different. A primality... OP wants something different. A primality certificate for Mersenne primes, so a (very) fast proof when 2^p-1 is prime (where p is an odd prime). Let r=2+sqrt[3] and calculate v=r^(2^(p-2)) in...
 Forum: Homework Help 2021-11-20, 16:37 Replies: 23 Views: 4,017 Posted By R. Gerbicz That is... That is https://en.wikipedia.org/wiki/Euler%27s_theorem for m=p^n. When you want the best exponent for all gcd(a,n)=1 it is also a known problem (n=168 in your case). Let...
 Forum: Miscellaneous Math 2021-11-16, 14:18 Replies: 7 Views: 257 Posted By R. Gerbicz For any p the e values is not lower bounded: ... For any p the e values is not lower bounded: set say x=1, then x^2*(x^3+y^3)=y^3+1 goes to -inf for y->-inf. For your 2nd question: about solving the equation for a given n=p+e: x^2*(x^3+y^3)=n...
 2021-11-15, 21:28 Replies: 30 Views: 5,607 Posted By R. Gerbicz Yeah, you're really messed up with a trivial... Yeah, you're really messed up with a trivial algorithm, a corrected one: (here you don't need to use ptr, so pointers, but give a clean code) void mpz_mod_mp (mpz_ptr r, mpz_ptr a, mp_bitcnt_t p)...
 Forum: Information & Answers 2021-11-15, 17:50 Replies: 17 Views: 1,007 Posted By R. Gerbicz Nice, not remembered for this, but for "large" n... Nice, not remembered for this, but for "large" n the k*2^n-1+1,+5 formula shouldn't be winning due to the slightly faster prp tests on special form? You would need T(N)=O(log(N)^5/loglog(N)^2) bit...
 Forum: Puzzles 2021-11-15, 15:12 Replies: 31 Views: 15,435 Posted By R. Gerbicz Thanks for the idea, then I'll try the AMM first,... Thanks for the idea, then I'll try the AMM first, need to write down the solution. It is a somewhat recreational Maths problem, but worth a paper.
 Forum: Homework Help 2021-11-15, 14:57 Replies: 2 Views: 286 Posted By R. Gerbicz You want this page from Iron Age:... You want this page from Iron Age: https://primes.utm.edu/notes/faq/NextMersenne.html for even(!) perfect numbers you get a similar graph, since P(k)=2^(p-1)*(2^p-1)~0.5*Mp^2 and for that...
 Forum: Factoring 2021-11-09, 22:00 Replies: 17 Views: 834 Posted By R. Gerbicz Much better: sieve and search only b=k*2^762... Much better: sieve and search only b=k*2^762 for k>10^15 (you can limit to say k<2^64). This will be good since now b is easily fully factored (you need to factor only k, but that is trivial). and...
 Forum: Software 2021-11-06, 15:54 Replies: 10 Views: 706 Posted By R. Gerbicz I'm not sure what your code is doing, anyway, for... I'm not sure what your code is doing, anyway, for a fixed B bound and e>1, solve the x*log(x)/e=B*log(B) equation, say binary search is fine since x*log(x) is monotone increasing (on [exp(-1),inf)...
 Forum: Software 2021-11-04, 18:09 Replies: 10 Views: 706 Posted By R. Gerbicz correction: log2(T)=187.0 sum(1/q^e)=0.00018 ... correction: log2(T)=187.0 sum(1/q^e)=0.00018 and effective score=995837.4 what is smaller than the base score: log2(B)*B=1660964.05
 Forum: Software 2021-11-04, 17:16 Replies: 10 Views: 706 Posted By R. Gerbicz Today multiple times I felt the same, but... Today multiple times I felt the same, but currently I think that this is a working idea, even in P+1/ecm ! Would give a tiny speedup. Let me check my suggestion. In the general way: for a given...
 Forum: Puzzles 2021-11-02, 10:51 Replies: 31 Views: 15,435 Posted By R. Gerbicz There was a request to explain this more, took me... There was a request to explain this more, took me some time to understand some tricks. First why parity is so important here. It is trivial: for each c=-24..24 we choose T(c,0) or T(c,1), exactly...
 Forum: Software 2021-10-25, 18:25 Replies: 594 Views: 86,637 Posted By R. Gerbicz Just for curiosity that is is how many k/n pairs,... Just for curiosity that is is how many k/n pairs, so what is the #k * (nmax-nmin) ?
 Forum: MattcAnderson 2021-10-18, 20:17 Replies: 24 Views: 991 Posted By R. Gerbicz Still in high school's math camp we constructed a... Still in high school's math camp we constructed a regular 17-gon. There is an elementary way to show that if you can make a regular m and n-gon [using straightedge and compass] and gcd(m,n)=1...
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