I think (wish) I find a new prime number record

[Glenio]

Originally Posted by kriesel

P-1 to full PrimeNet bounds on M102589933 under way here, will complete in hours. https://www.mersenne.ca/exponent/102589933 says 5.6% probability of factor, no p-1 result reported yet. It would be silly to have primality tested it without doing that first.
Maybe he meant a Fermat number. That claim would be safe from computational attack for a while.
As stated in his post, a large power of two being prime, it's too absurd a claim to even bother including in the count in the "dubious claims" list behind the stats in https://www.mersenneforum.org/showpo...04&postcount=5

There are few rhyming prime exponents surviving even cursory TF above M82589933.
102589933 NF 74, further TF assigned to gpu72, P-1 underway
112589933 small factor
222589933 small factor
232589933 NF 71, go to 79 assigned, no p-1 yet 2290000,68700000
312589933 small factors
532589933 smallish factor
612589933 smallish factor
642589933 NF 70, go to 84 assigned, no p-1 yet 5740000,172200000
652589933 NF 71, go to 84 assigned, no p-1 yet 5820000,174600000
672589933 smallish factors
702589933 small factors
892589933 smallish factor
912589933 smallish factor
952589933 small factors
(up to 999M)

The 3 other survivors are being addressed with TF and may get some P-1 attention after.

70237298350549551468899 á is congruent with 1 (mod 4) and no cofactor is also known; therefore, there may still be a chance that 2 ^ 70237298350549551468899-1 is prime. This is just an example that I am taking into account.

[paulunderwood]

Originally Posted by Glenio

70237298350549551468899 á is congruent with 1 (mod 4) and no cofactor is also known; therefore, there may still be a chance that 2 ^ 70237298350549551468899-1 is prime. This is just an example that I am taking into account.

Is it 3 mod 4?

How many tons of coal are needed to LL test it?

What do you calculate the "chance" of being prime is?

Let me give you an example prime p=2^82589933-1 definitely has no small factors. So is 2^p-1 prime? Anyone?

[Batalov]

Originally Posted by Glenio

This is the number 2^102589933

.

[kriesel]

Originally Posted by Glenio

70237298350549551468899 á is congruent with 1 (mod 4) and no cofactor is also known; therefore, there may still be a chance that 2 ^ 70237298350549551468899-1 is prime. This is just an example that I am taking into account.

That reply to my post has nothing to do with my post. It's a ~75.89 bit exponent, making the corresponding Mersenne number untestable for primality or P-1 factoring in existing software, or realistic hardware lifetime or memory capacity, and is only factorable by slow cpu TF. But it earns a spot in the dubious-claims list, for which the track record is zero primes proven to date of several dozen entries; a handful yet to be resolved.

[kladner]

Wouldn't this be at home in:

http://primes.utm.edu/notes/crackpot.html
Miscellaneous Math?

[masser]

Originally Posted by kladner

Wouldn't this be at home in:

http://primes.utm.edu/notes/crackpot.html
Miscellaneous Math?

seconded.

[Kalli Hofmann]

What do you claim ? :
Is 2 ^ 70237298350549551468899 – 1 a prime Number ?
or is 2 ^ 102589933 – 1 a prime Number ?
Please be accurate with your claims.

[Dylan14]

Originally Posted by Kalli Hofmann

What do you claim ? :
Is 2 ^ 70237298350549551468899 – 1 a prime Number ?
or is 2 ^ 102589933 – 1 a prime Number ?
Please be accurate with your claims.

With the first number - I used factor5 to test factors up to 2^110. No factors found. This doesn't mean that it is prime, because in order to test that this number is prime, I would need the LL test, but this number is far beyond anyone's compute power. Not going to bother testing it farther...
With regards to the second - someone is running a PRP test on it. Assuming the machine that is running it is being run 24/7 on this number and it is a reasonably modern machine, we should know within a few weeks whether it is probably prime (in which case it will be tested with LL to conclude definitively whether it is prime) or not (in which case it's composite).

[Kalli Hofmann]

Going to 111,67 bit but still no factor. Going further a little bit.

[Jan S]

M102589933 is(probably) not prime. I tested with GPUowl.

[Uncwilly]

Thanks, we can now leave this to rest in peace.