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

[Batalov]

Originally Posted by Jan S

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

That's not how a PRP test is interpreted. If the test is negative - there is nothing probable about it. Then the number simply is composite.

Only if the test is positive, then the number is probably prime.

[retina]

Originally Posted by Batalov

That's not how a PRP test is interpreted. If the test is negative - there is nothing probable about it. Then the number simply is composite.

Only if you assume the test was run perfectly without any coding bugs or subtle system problems. And that the poster is upstanding and forthright without any agenda towards deception.

[paulunderwood]

Originally Posted by Batalov

That's not how a PRP test is interpreted. If the test is negative - there is nothing probable about it. Then the number simply is composite.

Only if the test is positive, then the number is probably prime.

Another test needs to be done to get matching residue. There remains a non-zero chance that the number is prime. Maybe something like 1/2^10000 considering how fantastically accurate GEC is

[Uncwilly]

I bet Ken is on it as we speak.

[Batalov]

Originally Posted by paulunderwood

There remains a non-zero chance that the number is prime. Maybe something like 1/2^10000 considering how fantastically accurate

.

[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.

How far has 2^{70237298350549551468899}-1 been factored?

[kriesel]

Originally Posted by kladner

Wouldn't this be at home in:

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

My sediments exactly.

[Uncwilly]

Originally Posted by kriesel

How far has 2^{70237298350549551468899}-1 been factored?

It is not worth anybody's time, expect the OP to worry about that.
2^110 per https://mersenneforum.org/showpost.p...5&postcount=19

[kriesel]

Originally Posted by Uncwilly

I bet Ken is on it as we speak.

I left M102589933 alone, since when I checked it earlier, it was reserved to GPU72. Then it progressed rapidly to a conclusion.
102589933 NF to 77 bits, P-1 NF, PRP C, eliminated (Thanks Jan S et al)

As a preemptive effort regarding further rhyming exponent claims, the few survivors have been taken a bit further
232589933 NF to 79 bits, P-1 NF, PRP assigned (queued in gpuowl on a radeon vii)
642589933 NF to 84 bits, P-1 in progress to B1=5740000,B2=172200000 (prime95 on i7-4790)
652589933 NF to 84 bits, P-1 in progress to B1=5820000,B2=174600000 (gpuowl on radeon vii)

M70237298350549551468899 I've done from zero, NF to 123 bits (Ernst's mfactor program took ~44 hours with 16 processes on a dual-12-core-xeon-e5-2697 to do 122-123 bits, with only ~15% impact on prime95 throughput thanks to hyperthreading; any further progress on it will be posted in https://www.mersenneforum.org/showpo...04&postcount=5. This one is wildly out of reach of P-1 or primality testing, due to estimated file size, estimated memory requirements, software suitability, and run time projections)

[kriesel]

An update on the 7-digit decimal rhyme exponent Mersennes of Mp51*, p=82589933:
232589933 NF to 79 bits, P-1 NF, PRP composite, eliminated

Still in the running as possible rhyming exponent primes:
642589933 NF to 84 bits, P-1 NF
652589933 NF to 84 bits, P-1 NF
These would each take about as long to primality test as fifty 100M wavefront exponents.

[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.

This (non sequitur to our collective debunking of the dubious claim that 2^102589933 was prime) has been trial factored to 125 bits in Ernst's Mfactor program with no factor found. Its odds of being prime are nevertheless quite low. If I take it further someday, the status will update at https://www.mersenneforum.org/showpo...04&postcount=5