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

Glenio 2020-05-23 18:03

Prime Number
 
[QUOTE=kriesel;546295]P-1 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 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 [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, P-1 underway
112589933 small factor
222589933 small factor
[M]232589933[/M] NF 71, go to 79 assigned, no p-1 yet 2290000,68700000
312589933 small factors
532589933 smallish factor
612589933 smallish factor
[M]642589933[/M] NF 70, go to 84 assigned, no p-1 yet 5740000,172200000
[M]652589933[/M] 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.[/QUOTE]
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 2020-05-23 18:38

[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 ^ 70237298350549551468899-1 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=2^82589933-1 definitely has no small factors. So is 2^p-1 prime? Anyone?

:crank:

Batalov 2020-05-23 18:58

1 Attachment(s)
[QUOTE=Glenio;546287]This is the number 2^102589933[/QUOTE][COLOR="LemonChiffon"].[/COLOR]

kriesel 2020-05-23 21:26

[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 ^ 70237298350549551468899-1 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 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 2020-05-23 22:04

Wouldn't this be at home in:

[url]http://primes.utm.edu/notes/crackpot.html[/url]
Miscellaneous Math?:confused2:

masser 2020-05-23 23:25

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

[url]http://primes.utm.edu/notes/crackpot.html[/url]
Miscellaneous Math?:confused2:[/QUOTE]

seconded.

Kalli Hofmann 2020-05-24 19:52

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 2020-05-25 20:43

[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]

Kalli Hofmann 2020-05-26 11:18

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

Jan S 2020-05-30 09:31

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

Uncwilly 2020-05-30 13:59

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


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