fond of a factor? Urn yourself to become remains

[ET_]

Originally Posted by ckdo

Correct.


There are 308,457,624,821 primes that are 13 digits in length, of which your k is one.

True, but think about this: prime95 sieving code factors out 95% of possible factors, and you get 1:3,000,000,000 chances...


Luigi

[ckdo]

Originally Posted by ET_

True, but think about this: prime95 sieving code factors out 95% of possible factors, and you get 1:3,000,000,000 chances...

Luigi

This thread alone has two prime k values. Reconsider.

[cheesehead]

Originally Posted by ckdo

This thread alone has two prime k values. Reconsider.

"Prime" is just one of GIMPS's middle names!

[wblipp]

Originally Posted by drh

From TF -
M76941257 has a factor: 1037510862086650011527

K = 6742227138859 and is Prime ...

This is the first K that I've found like this, unless I messed up my calcs somewhere. Just curious if this is very common or not.

I would expect the k's to be prime about as often as random integers of the same size, and I expect that to be about one in ln(k) - around 3% in this case. So not frequent, but not particularly rare either.

[ckdo]

M6881183 has a factor: 3318239732112217940854822409556994849914743184848593 (172 bits)

3318239732112217940854822409556994849914743184848593 = 5197536752361631481431 (73 bits) * 638425448478934238065804225303 (100 bits)

k1 = 3^2 * 5 * 11 * 19 * 43 * 223 * 4187669
k2 = 3 * 7 * 31^2 * 241 * 349 * 379 * 28909 * 2494363

P-1, B1=435000, B2=13158750, E=12

[Batalov]

Originally Posted by cmd

=792=

.. 9901 .. 99990001 .. 999999000001 ..

This are primes, so what. You will frequently get a lot of them for a factorization of a random large (10^3n-1)/9 or 10^3n+1. They are Phi₁₂(10), Phi₂₄(10), and Phi₃₆(10).

You haven't seen 9999999900000001 yet? That's Phi₄₈(10).

[gd_barnes]

Originally Posted by ckdo

Correct.


There are 308,457,624,821 primes that are 13 digits in length, of which your k is one.

308,457,624,821 is prime

[alpertron]

Another factor found when running ECM at the 30-digit level:

Originally Posted by results.txt

ECM found a factor in curve #87, stage #2
Sigma=971829533210027, B1=250000, B2=25000000.
M600101 has a factor: 93081705403274340410364699761

Since k = 2^3 x 5 x 31 x 43 x 1454520493977573859, it could not have been found using p-1.

[lorgix]

Stop spamming.

[ckdo]

M410009 has a factor: 573233658698571372455711

k = 5 * 139810018487050619

[moebius]

M332254913 has a factor: 5308157432898908836177
found 1 factor(s) for M332254913 from 2^72 to 2^73 [mfaktc 0.16p1 barrett79_mul32]