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 Showing results 1 to 25 of 748 Search took 0.10 seconds. Search: Posts Made By: charybdis
 Forum: Software 2022-06-27, 11:48 Replies: 4 Views: 114 Posted By charybdis Yes (I assume you meant a(p-1)/2). For k*2^n+1... Yes (I assume you meant a(p-1)/2). For k*2^n+1 this requires ~n squarings, hence the n iterations that LLR performs.
 Forum: Software 2022-06-27, 11:12 Replies: 4 Views: 114 Posted By charybdis By Euler's criterion... By Euler's criterion (https://en.wikipedia.org/wiki/Euler%27s_criterion), if p is prime, then a(p-1)/2 is 1 mod p if a is a square mod p, and -1 mod p if a is not a square mod p. So it suffices to...
 Forum: NFS@Home 2022-06-26, 23:48 Replies: 141 Views: 16,413 Posted By charybdis QUEUED AS 2_2694L 2,2694L is another c204... QUEUED AS 2_2694L 2,2694L is another c204 from the Cunningham project that is ready for GNFS on 16e-small. n:...
 Forum: Miscellaneous Math 2022-06-26, 19:10 Replies: 28 Views: 612 Posted By charybdis The theorem that says a polynomial has at most as... The theorem that says a polynomial has at most as many roots as its degree only holds over integral domains, i.e. rings in which it is impossible for two non-zero elements to multiply to zero....
 Forum: Miscellaneous Math 2022-06-25, 01:24 Replies: 8 Views: 114 Posted By charybdis Well apparently they don't. Yafu does: $... Well apparently they don't. Yafu does:$ yafu "factor(37598509921358937130067447226996383490394965883350770227491949626316296206227551680872850721799316915254863210166862451532957886446390226981)"...
 Forum: Miscellaneous Math 2022-06-24, 23:19 Replies: 8 Views: 114 Posted By charybdis I used PARI: gp > \p 400 realprecision... I used PARI: gp > \p 400 realprecision = 404 significant digits (400 digits displayed) gp >...
 Forum: Miscellaneous Math 2022-06-24, 22:36 Replies: 28 Views: 612 Posted By charybdis :smile: You might have got this confused... :smile: You might have got this confused with the proof that e is irrational, which is much simpler - I seem to recall being set it as an exercise as a first-year undergraduate.
 Forum: Miscellaneous Math 2022-06-24, 21:40 Replies: 28 Views: 612 Posted By charybdis This is the definition of e^11... This is the definition of e^11...
 Forum: Miscellaneous Math 2022-06-24, 21:39 Replies: 8 Views: 114 Posted By charybdis Fermat's method. It works on the first try. Fermat's method. It works on the first try.
 Forum: MattcAnderson 2022-06-23, 21:52 Replies: 5 Views: 109 Posted By charybdis If k is odd, then x^k+1 factorizes as... If k is odd, then x^k+1 factorizes as (x+1)(x^(k-1)-x^(k-2)+...-x+1). Substituting 10^m for x, we see that 10^km+1 is divisible by 10^m+1 if k is odd. In other words, 10^n+1 cannot be prime if n has...
 Forum: Factoring 2022-06-22, 16:42 Replies: 501 Views: 76,706 Posted By charybdis Usual warning that you can't directly compare... Usual warning that you can't directly compare E-scores for polys with different degrees. Lower degrees overpeform their scores, higher degrees underperform.
 Forum: Factoring 2022-06-22, 14:35 Replies: 501 Views: 76,706 Posted By charybdis Correct for the second one, but not the first. ... Correct for the second one, but not the first. 288 = 2*3*47, so 13^288+1 has algebraic factors 13^94+1 and 13^6+1, which themselves share a common factor 13^2+1. We can't pull out both algebraic...
 Forum: Factoring 2022-06-22, 13:03 Replies: 501 Views: 76,706 Posted By charybdis Yes, both exponents are divisible by 3 so you can... Yes, both exponents are divisible by 3 so you can divide out the algebraic factors 13^94+1 and 13^96+1 respectively. So you have to multiply the size of the number by 2/3 to get the actual difficulty.
 Forum: NFS@Home 2022-06-15, 16:47 Replies: 62 Views: 4,272 Posted By charybdis Yes. More relations = more time spent in... Yes. More relations = more time spent in duplicate, singleton and clique removal.
 Forum: FactorDB 2022-06-15, 15:16 Replies: 561 Views: 105,428 Posted By charybdis It is his current address. He probably didn't... It is his current address. He probably didn't reply to you because your suggestions were unnecessary and/or stupid.
 Forum: Msieve 2022-06-13, 18:55 Replies: 2,217 Views: 221,435 Posted By charybdis 2,2694L Ran up to admax=50M. These aren't quite Gimarel-standard but they're okay: n:...
 Forum: Cunningham Tables 2022-06-12, 16:10 Replies: 26 Views: 10,735 Posted By charybdis Hmmm, can you point me to a reference for this?... Hmmm, can you point me to a reference for this? Surely the optimum ratio is implementation dependent?
 Forum: Aliquot Sequences 2022-06-12, 14:14 Replies: 1,718 Views: 198,315 Posted By charybdis The other consequence of the (b^n-1)/(b-1)... The other consequence of the (b^n-1)/(b-1) observation is, of course, that SNFS can be used on term 1 for prime bases.
 Forum: Aliquot Sequences 2022-06-12, 13:26 Replies: 1,718 Views: 198,315 Posted By charybdis If the base b is prime, then term 1 of sequence... If the base b is prime, then term 1 of sequence b^n will be b^(n-1) + b^(n-2) + ... + b + 1 = (b^n-1)/(b-1). Since b^n-1 divides all numbers of the form b^kn-1, this naturally leads to shared factors...
 Forum: Msieve 2022-06-09, 17:25 Replies: 2,217 Views: 221,435 Posted By charybdis Gonna do some CADO polyselect on 2,2694L c204.... Gonna do some CADO polyselect on 2,2694L c204. P=5M, incr=420, starting at admin=5M, haven't decided how far I'll go.
 Forum: Factoring 2022-06-09, 16:38 Replies: 12 Views: 587 Posted By charybdis CADO-NFS should run on a Mac (edit: possibly not... CADO-NFS should run on a Mac (edit: possibly not an ARM one?), though I have no experience in this regard. The readme contains some specifics about installation on Macs, e.g. needing to install wget...
 Forum: Factoring 2022-06-09, 01:44 Replies: 68 Views: 1,396 Posted By charybdis Not an electrical engineer so I have no clue what... Not an electrical engineer so I have no clue what you're on about. Unless this is just chalsall code for "are you an electrical engineer?" in which case you've got your answer. Never mind...
 Forum: Factoring 2022-06-09, 00:41 Replies: 68 Views: 1,396 Posted By charybdis I don't know where you're getting the term... I don't know where you're getting the term "exclusion" from. It's an instruction to GMP-ECM saying "I've already run stage 1 with B1=8e8, so please run stage 2 with the appropriate B2". Excuse...
 Forum: NFS@Home 2022-06-08, 18:12 Replies: 20 Views: 565 Posted By charybdis Yeah, you'll be fine. As a rule of thumb, matrix... Yeah, you'll be fine. As a rule of thumb, matrix solving time roughly multiplies by 4.5 for each doubling of the matrix dimensions.
 Forum: Factoring 2022-06-08, 17:13 Replies: 68 Views: 1,396 Posted By charybdis What exactly were you trying to do?... What exactly were you trying to do? "B1=50000000-49000000" is totally meaningless from a theoretical point of view. Why would anyone even think of trying it? And what do you mean by an exclusion??...
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