[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. 
[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]

[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 nonzero chance that the number is prime. Maybe something like 1/2^10000 considering how fantastically accurate GEC is :wink: 
I bet Ken is on it as we speak.

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[QUOTE=paulunderwood;546846]There remains a nonzero chance that the number is prime. Maybe something like 1/2^10000 considering how fantastically accurate [/QUOTE]
[COLOR="LemonChiffon"].[/COLOR] 
[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 ^ 702372983505495514688991 is prime. This is just an example that I am taking into account.[/QUOTE]How far has 2[SUP]70237298350549551468899[/SUP]1 been factored?

[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. 
[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] 
[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, P1 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, P1 NF, PRP assigned (queued in gpuowl on a radeon vii) [M]642589933[/M] NF to 84 bits, P1 in progress to B1=5740000,B2=172200000 (prime95 on i74790) [M]652589933[/M] NF to 84 bits, P1 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 dual12corexeone52697 to do 122123 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 P1 or primality testing, due to estimated file size, estimated memory requirements, software suitability, and run time projections) 
An update on the 7digit decimal rhyme exponent Mersennes of Mp51*, p=82589933:
[M]232589933[/M] NF to 79 bits, P1 NF, PRP composite, eliminated Still in the running as possible rhyming exponent primes: [M]642589933[/M] NF to 84 bits, P1 NF [M]652589933[/M] NF to 84 bits, P1 NF These would each take about as long to primality test as fifty 100M wavefront exponents. 
[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 ^ 702372983505495514688991 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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