Forum: Miscellaneous Math
2022-06-25, 01:24
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Replies: 8
Views: 103
Well apparently they don't. Yafu does:
$...
Well apparently they don't. Yafu does:
$ yafu "factor(37598509921358937130067447226996383490394965883350770227491949626316296206227551680872850721799316915254863210166862451532957886446390226981)"...
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Forum: Miscellaneous Math
2022-06-24, 23:19
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Replies: 8
Views: 103
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Forum: Miscellaneous Math
2022-06-24, 22:36
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Replies: 23
Views: 456
: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.
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Forum: Miscellaneous Math
2022-06-24, 21:40
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Replies: 23
Views: 456
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Forum: Miscellaneous Math
2022-06-24, 21:39
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Replies: 8
Views: 103
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Forum: MattcAnderson
2022-06-23, 21:52
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Replies: 5
Views: 102
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...
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Forum: Factoring
2022-06-22, 16:42
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Replies: 500
Views: 76,494
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Forum: Factoring
2022-06-22, 14:35
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Replies: 500
Views: 76,494
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Forum: Factoring
2022-06-22, 13:03
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Replies: 500
Views: 76,494
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Forum: NFS@Home
2022-06-15, 16:47
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Replies: 61
Views: 4,214
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Forum: FactorDB
2022-06-15, 15:16
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Replies: 561
Views: 105,267
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Forum: Msieve
2022-06-13, 18:55
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Replies: 2,217
Views: 221,009
2,2694L
Ran up to admax=50M. These aren't quite Gimarel-standard but they're okay:
n:...
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Forum: Cunningham Tables
2022-06-12, 16:10
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Replies: 26
Views: 10,665
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Forum: Aliquot Sequences
2022-06-12, 14:14
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Replies: 1,707
Views: 197,544
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Forum: Aliquot Sequences
2022-06-12, 13:26
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Replies: 1,707
Views: 197,544
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...
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Forum: Msieve
2022-06-09, 17:25
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Replies: 2,217
Views: 221,009
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Forum: Factoring
2022-06-09, 16:38
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Replies: 11
Views: 454
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Forum: Factoring
2022-06-09, 01:44
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Replies: 68
Views: 1,319
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Forum: Factoring
2022-06-09, 00:41
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Replies: 68
Views: 1,319
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...
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Forum: NFS@Home
2022-06-08, 18:12
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Replies: 20
Views: 556
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Forum: Factoring
2022-06-08, 17:13
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Replies: 68
Views: 1,319
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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Forum: Factoring
2022-06-08, 00:59
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Replies: 68
Views: 1,319
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...
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Forum: Factoring
2022-06-07, 20:46
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Replies: 68
Views: 1,319
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...
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Forum: Factoring
2022-06-07, 17:46
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Replies: 68
Views: 1,319
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Forum: Factoring
2022-06-07, 14:33
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Replies: 68
Views: 1,319
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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