fond of a factor? Urn yourself to become remains

[prgamma10]

Originally Posted by Miszka

My personal best
M31051 has a factor: 24523881623890845010007531389564120430998338703 (154,1 bits)
ECM found a factor in curve #24, stage #2
Sigma=3677350809829694, B1=3000000, B2=300000000

Tasty factor, considering the ECM bounds used.

[blahpy]

Originally Posted by Miszka

My personal best
M31051 has a factor: 24523881623890845010007531389564120430998338703 (154,1 bits)
ECM found a factor in curve #24, stage #2
Sigma=3677350809829694, B1=3000000, B2=300000000

Very nice!

[lycorn]

Originally Posted by Miszka

M31051 has a factor: 24523881623890845010007531389564120430998338703

Very nice one. It´s not every day that one finds factors for numbers this small...

[TheJudger]

Hello,

IIRC this is my second biggest "regular P-1 factor":
P-1 found a factor in stage #2, B1=620000, B2=12710000, E=12.
M67894507 has a factor: 118932379415737719145680729417648731019161 (136.44 Bits)
k = 875861573129455959859026072739940 = 2 * 2 * 5 * 19 * 2897 * 15667 * 214589 * 283697 * 370423 * 2251943

and this might be my biggest "regular P-1 double factor" so far:
P-1 found a factor in stage #1, B1=635000.
M66012833 has a factor: 25442648702559071526003179150718822132839669303705434471 (184.05 Bits)

f₁ = 93709867836738562740151 (76.31 Bits)
k₁ = 3 * 5 * 5 * 8641 * 11071 * 98927

f₂ = 271504477488809212102512933946321 (107.74 Bits)
k₂ = 2 * 2 * 2 * 3 * 5 * 43 * 137 * 5737 * 27823 * 54217 * 336143


Oliver

[markr]

Those are massive - nice finds!

[Batalov]

Mike Oakes described many years ago the Eisenstein-Fermat numbers.

Mike Oakes reported that EF_n are prime for 0<=n<=3, and then we have composites up to n<=19 (DC'd).
Here are some more eliminations:

1814704020258817 | 3^(2^20)-3^(2^19)+1
449939767297 | 3^(2^21)-3^(2^20)+1
EF22 LLR test is in progress (most likely known C)
EF23 LLR test is in progress (most likely known C)
841781914632193 | 3^(2^24)-3^(2^23)+1
10871635969 | 3^(2^25)-3^(2^24)+1
EF26 ??
3819992499879937 | 3^(2^27)-3^(2^26)+1
EF28 ??
156071646883479553 | 3^(2^29)-3^(2^28)+1
...
5566277615617 | 3^(2^32)-3^(2^31)+1
131985100920324097 | 3^(2^34)-3^(2^33)+1
39582418599937 | 3^(2^38)-3^(2^37)+1

(you can easily see that factors are of restricted form. Not too hard to find.)

[Sergiosi]

From one of my aliquot sequences:

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1045294942
Step 1 took 5593ms
Step 2 took 2784ms
********** Factor found in step 2: 7709785821798716085231895649922705932140748936402071
Found probable prime factor of 52 digits: 7709785821798716085231895649922705932140748936402071
Probable prime cofactor (679244561234214691156167254744998224687295035638998699333453501573680827350025562911300646832911553455921867383084123581660457/55577579143)/7709785821798716085231895649922705932140748936402071 has 64 digits

[ET_]

Originally Posted by Sergiosi

From one of my aliquot sequences:

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1045294942
Step 1 took 5593ms
Step 2 took 2784ms
********** Factor found in step 2: 7709785821798716085231895649922705932140748936402071
Found probable prime factor of 52 digits: 7709785821798716085231895649922705932140748936402071
Probable prime cofactor (679244561234214691156167254744998224687295035638998699333453501573680827350025562911300646832911553455921867383084123581660457/55577579143)/7709785821798716085231895649922705932140748936402071 has 64 digits

The cofactor is a certified prime.

Luigi

[alpertron]

At this moment I'm running p-1 algorithm with B1=10M, B2=500M in the range 900000-1000000.

My computer found a new personal record:

P-1 found a factor in stage #2, B1=10000000, B2=500000000, E=12.
M985979 has a factor: 208259944761322336790033394725144178055361063

More details about this Mersenne number at: http://www.mersenne.ca/exponent/985979

[lycorn]

A somehow unexpected finding from my old snail:

UID: lycorn/snail, M947857 has a factor: 4558968051813269609

61.983 bits
K=2^2 × 601220444093 => P-1 had obviously missed it...

[PageFault]

My first ECM find:

[Wed Jun 11 22:35:04 2014]
ECM found a factor in curve #6, stage #1
Sigma=1167748058492201, B1=50000, B2=5000000.
UID: PageFault/boxen_40, M9178789 has a factor: 64337196736770344347561

k = 2^2 × 3 × 5 × 17 × 61 × 373 × 151010767

May there be many more ...