And another one...

UID: lycorn/asteroid, M701179 has a factor: 62175023660062474016743 (ECM curve 23, B1=250000, B2=25000000)

[B]75.719[/B] bits

This one had been missed @ B1=50,000.

What is the largest [smallest factor of a Mersenne-Pseudoprime (the ones with prime exponents) ] ever found?

To clarify, looking for the equivalents of 23 and not 89 or 2047 for M11 of any Mersenne-Pseudoprime which is the largest ever found.
Thanks in advance.

[QUOTE=a1call;482102]What is the largest [smallest factor of a Mersenne-Pseudoprime (the ones with prime exponents) ] ever found?

To clarify, looking for the equivalents of 23 and not 89 or 2047 for M11 of any Mersenne-Pseudoprime which is the largest ever found.
Thanks in advance.[/QUOTE]

Have a look in here: [url]https://eprint.iacr.org/2014/653.pdf[/url]

[QUOTE=VBCurtis;482119]Have a look in here: [URL]https://eprint.iacr.org/2014/653.pdf[/URL][/QUOTE]

Thank you VBCurtis.

I did not get result from that link.

Some of the 17 exponents are not prime. The ones that are and I checked, report enormous factors of Mersennes with also much smaller factors such as:


[URL]https://www.mersenne.org/report_exponent/?exp_lo=1129&exp_hi=[/URL]

Thanks for the reply though.:smile:

ETA the largest, smallest factor seems to be here (from the list of 17)
[url]https://www.mersenne.org/report_exponent/?exp_lo=1123&exp_hi=[/url]

I doubt that is the largest ever found.

Ah, sorry; I was thinking of "largest penultimate", rather than largest smallest-factor.
I queried factordb; 2^727-1 has P98, while 2^1061-1 has P143. I searched up to 1200, since no SNFS has been done above 1200 and ECM can't find factors over P90 (well, hasn't yet done so!).

[QUOTE=VBCurtis;482129]Ah, sorry; I was thinking of "largest penultimate", rather than largest smallest-factor.
I queried factordb; 2^727-1 has P98, while 2^1061-1 has P143. I searched up to 1200, since no SNFS has been done above 1200 and ECM can't find factors over P90 (well, hasn't yet done so!).[/QUOTE]

Wow, thank you very much sir.
Wished I knew how to do the search myself.
Sorry for my nonmathematician ignorance, but which method has factored M1061? is that SNFS?

"LL verified factored"
Are they factored using LL test?

Let p=2618163402417 * 2^1290000-1

Let q=2*p+1 = 2618163402417 * 2^1290001-1

Both p&q are prime, and q | Mp ([url]http://primes.utm.edu/top20/page.php?id=2[/url])

That's kind of like starting with a factor and finding a product thing. Without a limit on the upper bound of the exponents, there can be very large factors (reverse) found.
My main interest was knowing which factorization method was likely to yield result for smallish exponents such as 1277.
Thank you for all the replies.

Still, that's a very big factor.:smile:

More to follow, I hope,

UID: lycorn/asteroid, M[B]701279[/B] has a factor: [B]109524525600903796107001439[/B] (ECM curve 6, B1=250000, B2=25000000),

k = 7 × 89459 × 124700579539997

86.5 bits

I ran P-1 for [URL="https://www.mersenne.org/report_exponent/?exp_lo=2348581&full=1"]M2348581[/URL] with B1 = 500000, B2 = 15M and the computer found the factor 5548683844149279840865697.

k = 2[sup]4[/sup] × 269 × 391057 × [b]701846461[/b]

The largest prime factor of k is 46.8 times greater than B2.

Early this morning:

UID: lycorn/asteroid, [B]M701837[/B] has a factor: [B]259854790206125142269983759[/B] (ECM curve 143, B1=250000, B2=25000000),

k =3 × 3653737 × 16889077695097

87.7 bits