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-   -   I think (wish) I find a new prime number record (https://www.mersenneforum.org/showthread.php?t=25562)

 Batalov 2020-05-31 01:04

[QUOTE=Jan S;546795]M102589933 is [COLOR="Red"](probably)[/COLOR] not prime. I tested with GPUowl.[/QUOTE]
That's not how a PRP test is interpreted. If the test is negative - there is nothing [I]probable [/I]about it. Then the number simply is composite.

Only if the test is positive, then the number is [I]probably [/I]prime.

 retina 2020-05-31 03:16

[QUOTE=Batalov;546841]That's not how a PRP test is interpreted. If the test is negative - there is nothing [I]probable [/I]about it. Then the number simply is composite.[/QUOTE]Only if you assume the test was run perfectly without any coding bugs or subtle system problems. [size=1]And that the poster is upstanding and forthright without any agenda towards deception.[/size]

 paulunderwood 2020-05-31 03:17

[QUOTE=Batalov;546841]That's not how a PRP test is interpreted. If the test is negative - there is nothing [I]probable [/I]about it. Then the number simply is composite.

Only if the test is positive, then the number is [I]probably [/I]prime.[/QUOTE]

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 :wink:

 Uncwilly 2020-05-31 03:45

I bet Ken is on it as we speak.

 Batalov 2020-05-31 05:53

1 Attachment(s)
[QUOTE=paulunderwood;546846]There remains a non-zero chance that the number is prime. Maybe something like 1/2^10000 considering how fantastically accurate [/QUOTE]
[COLOR="LemonChiffon"].[/COLOR]

 kriesel 2020-05-31 15:22

[QUOTE=Glenio;546306]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.[/QUOTE]How far has 2[SUP]70237298350549551468899[/SUP]-1 been factored?

 kriesel 2020-05-31 15:24

[QUOTE=kladner;546319]Wouldn't this be at home in:

[URL]http://primes.utm.edu/notes/crackpot.html[/URL]
Miscellaneous Math?:confused2:[/QUOTE]My sediments exactly.

 Uncwilly 2020-05-31 16:06

[QUOTE=kriesel;546877]How far has 2[SUP]70237298350549551468899[/SUP]-1 been factored?[/QUOTE]It is not worth anybody's time, expect the OP to worry about that.
2^110 per [url]https://mersenneforum.org/showpost.php?p=546425&postcount=19[/url]

 kriesel 2020-05-31 16:09

[QUOTE=Uncwilly;546847]I bet Ken is on it as we speak.[/QUOTE]I left M102589933 alone, since when I checked it earlier, it was reserved to GPU72. Then it progressed rapidly to a conclusion.
[M]102589933[/M] 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
[M]232589933[/M] NF to 79 bits, P-1 NF, PRP assigned (queued in gpuowl on a radeon vii)
[M]642589933[/M] NF to 84 bits, P-1 in progress to B1=5740000,B2=172200000 (prime95 on i7-4790)
[M]652589933[/M] 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 [URL]https://www.mersenneforum.org/showpost.php?p=512904&postcount=5[/URL]. 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 2020-10-09 16:42

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

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

 kriesel 2020-11-29 14:54

[QUOTE=Glenio;546306]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.[/QUOTE]This (non sequitur to our collective debunking of the dubious claim that 2[SUP]102589933[/SUP] 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 [url]https://www.mersenneforum.org/showpost.php?p=512904&postcount=5[/url]

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