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 Showing results 1 to 25 of 744 Search took 0.10 seconds. Search: Posts Made By: charybdis
 Forum: Miscellaneous Math 2022-06-25, 01:24 Replies: 8 Views: 103 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: 103 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: 23 Views: 456 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: 23 Views: 456 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: 103 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: 102 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: 500 Views: 76,494 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: 500 Views: 76,494 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: 500 Views: 76,494 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: 61 Views: 4,214 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: 105,267 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: 221,009 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: 10,665 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: 1,707 Views: 197,544 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: 1,707 Views: 197,544 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: 221,009 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: 11 Views: 454 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: 1,319 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: 1,319 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: 556 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: 1,319 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??...
 Forum: Factoring 2022-06-08, 00:59 Replies: 68 Views: 1,319 Posted By charybdis Apologies, you're right that it never shows a... Apologies, you're right that it never shows a range for B1 or B2 being specified *in the command line*. It only shows a command line without a range that produces output with a range. Then one can...
 Forum: Factoring 2022-06-07, 20:46 Replies: 68 Views: 1,319 Posted By charybdis Stage 1 and 2 each require some initialization... Stage 1 and 2 each require some initialization (computing the curve params from sigma, etc) and during this initialization some modular inversions are carried out mod N. GMP-ECM still runs these...
 Forum: Factoring 2022-06-07, 17:46 Replies: 68 Views: 1,319 Posted By charybdis Did you even read my post about what inputting a... Did you even read my post about what inputting a backwards range does? It literally doesn't run stage 1 at all. You can see this by inputting something stupid like 1e9-5e7 and it still "runs" stage 1...
 Forum: Factoring 2022-06-07, 14:33 Replies: 68 Views: 1,319 Posted By charybdis Yes: for a prime p, the group order is always... Yes: for a prime p, the group order is always within 2sqrt(p) of p+1, by Hasse's theorem. Of course the resulting B1/B2 that are guaranteed to find the factor are absurdly high for factors that we...
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