Prime Number
[QUOTE=kriesel;546295]P1 to full PrimeNet bounds on M102589933 under way here, will complete in hours. [URL]https://www.mersenne.ca/exponent/102589933[/URL] says 5.6% probability of factor, no p1 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 [URL]https://www.mersenneforum.org/showpost.php?p=512904&postcount=5[/URL] There are few rhyming prime exponents surviving even cursory TF above M82589933. [M]102589933[/M] NF 74, further TF assigned to gpu72, P1 underway 112589933 small factor 222589933 small factor [M]232589933[/M] NF 71, go to 79 assigned, no p1 yet 2290000,68700000 312589933 small factors 532589933 smallish factor 612589933 smallish factor [M]642589933[/M] NF 70, go to 84 assigned, no p1 yet 5740000,172200000 [M]652589933[/M] NF 71, go to 84 assigned, no p1 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 P1 attention after.[/QUOTE] 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=Glenio;546308]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]
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=2^825899331 definitely has no small factors. So is 2^p1 prime? Anyone? :crank: 
1 Attachment(s)
[QUOTE=Glenio;546287]This is the number 2^102589933[/QUOTE][COLOR="LemonChiffon"].[/COLOR]

[QUOTE=Glenio;546308]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]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 P1 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 dubiousclaims list, for which the track record is zero primes proven to date of several dozen entries; a handful yet to be resolved.

Wouldn't this be at home in:
[url]http://primes.utm.edu/notes/crackpot.html[/url] Miscellaneous Math?:confused2: 
[QUOTE=kladner;546319]Wouldn't this be at home in:
[url]http://primes.utm.edu/notes/crackpot.html[/url] Miscellaneous Math?:confused2:[/QUOTE] seconded. 
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. 
[QUOTE=Kalli Hofmann;546368]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.[/QUOTE] 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  [URL="https://www.mersenne.org/report_exponent/?exp_lo=102589933&full=1"]someone is running a PRP test on it[/URL]. 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).[URL="https://www.mersenne.org/report_exponent/?exp_lo=102589933&full=1"] [/URL] 
Going to 111,67 bit but still no factor. Going further a little bit.

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

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

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