fond of a factor? Urn yourself to become remains

[Jwb52z]

P-1 found a factor in stage #1, B1=665000.
UID: Jwb52z/Clay, M79429249 has a factor: 1841618282000258891653289 (P-1, B1=665000)

80.607 bits.

[GP2]

M5233 /2913486798065813495660442702490836503/32101013028243569/9223417954129/93603692660420120110355562102857/994271
is a new probable prime.

[LaurV]

Originally Posted by GP2

M5233 / 2913486798065813495660442702490836503 / 32101013028243569 / 9223417954129 / 93603692660420120110355562102857 / 994271
is a new probable prime.

That is an easily provable prime, it only has <1500 digits (no, I didn't make any calculus, and I didn't prove it yet, just a "first sight" mental evaluation).
I know that Dario already parsed this range, and it was no PRP there, therefore it means a new factor was found.
It can only be the biggest in your line.
Did you find the new factor by yourself?
Congratulations for the new factor, whoever found it.

edit, indeed this is new. I marked in red to be easy to see and inserted some spaces into that line

[Batalov]

Yes, it is new. Good find! You can email to S.S.W for extension tables.

[URL]http://primes.utm.edu/primes/search.php?Advanced=1[/URL] (use Official Comment=Mersenne cofactor, type=all, Maximum Number of Primes = 2000) => not there
Also: dated [URL="http://factordb.com/index.php?id=1100000000869501428"]Sep 29[/URL] in factordb.com

[Gordon]

Originally Posted by LaurV

That is an easily provable prime, it only has <1500 digits (no, I didn't make any calculus, and I didn't prove it yet, just a "first sight" mental evaluation).
I know that Dario already parsed this range, and it was no PRP there, therefore it means a new factor was found.
It can only be the biggest in your line.
Did you find the new factor by yourself?
Congratulations for the new factor, whoever found it.

edit, indeed this is new. I marked in red to be easy to see and inserted some spaces into that line

If you drill down through from the page you linked to, down to mersenne.ca it says it is fully factored and the remaining ~1500 digits are PRP.

Let's not reopen the PRP debate right now.

[LaurV]

Originally Posted by Gordon

If you drill down through from the page you linked to, down to mersenne.ca it says it is fully factored and the remaining ~1500 digits are PRP.

Let's not reopen the PRP debate right now.

That was nothing about reopening any debate, and I don't know anything about any "PRP debate". What is there to debate about PRPs?

Or you want to say that a ~1500 digits number is difficult to prove prime (or composite), with the hardware and the algorithms we have today?

[GP2]

Originally Posted by LaurV

That was nothing about reopening any debate, and I don't know anything about any "PRP debate". What is there to debate about PRPs?

I am also mystified. What is being debated about PRP?

I think the "debate" is about whether a probable prime cofactor means an exponent is truly "fully factored" or not. There was an old thread where people spent dozens of pages arguing vehemently over it. In this case it's a moot point, since this particular prime is easily within range of formal provability using primality certificates issued by primo or similar program.

A few weeks ago I started doing ECM on very small exponents with already known factor(s). Currently taking the M5000 range to B1=3,000,000 (i.e., "40 digits"), which means a few thousand curves per exponent.

So far I've found new factors for M4957, M5023, and M5233 (the latest result).

This has been just using Prime95, without GMP-ECM, but I will soon try that for stage 2.

Machines have gotten faster over the years and the time seems ripe to revisit this range in a thorough and systematic way. People have been throwing a lot of effort at the very stubborn M12xx holdouts, but there is some low-hanging fruit in the higher single-digit-thousands range.

So far I've been using only one core of a machine that's a few years old, but encouraged by this PRP result, I'm going to throw some more cores at it in the cloud. I've also been doing some ECM on already-factored exponents in the 40K and 50K ranges.

The most tedious part is creating the "known factors" string at the end of the ECM2= line, but I have a Python script that automates that.

[Jwb52z]

P-1 found a factor in stage #1, B1=665000.
UID: Jwb52z/Clay, M79423907 has a factor: 2357613551541984781291234249 (P-1, B1=665000)

90.929 bits.

[GP2]

Someone (not me) found a big one, the first known factor of M5879:

3381116440321017148580653633902983992991015840485797617951

58 digits, 192 bits.

[Miszka]

Originally Posted by GP2

Someone (not me) found a big one, the first known factor of M5879:

3381116440321017148580653633902983992991015840485797617951

58 digits, 192 bits.

It's my the best result

[snme2pm1]

I noticed that result also.
Impressive.
Plenty of bits.