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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 11:02

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

hello i'm new to the forum and i discovered a new prime number how do i claim the reward?

 retina 2020-05-23 11:41

[QUOTE=Glenio;546282][B][COLOR="Red"]hello i'm new to the forum and i discovered a new prime number how do i claim the reward?[/COLOR][/B][/QUOTE]The first step is to post your number for verification.

You won't get anything unless you show us your number is both large enough and is prime.

 Glenio 2020-05-23 11:48

Descobri um número primo maior que o atual

2^102589933:sorriso: já mandei a reedificação

[b][color=red][size=4]MODERATOR NOTE:[/size] Moved from "Mersenne prime in a Cunningham chain" thread.[/color][/b]

[b]Note on current status:[/b] (assuming poster meant 2^102589933 [b]- 1[/b]) Exponent status, No factors below 2[sup]74[/sup]

 pinhodecarlos 2020-05-23 11:55

 Glenio 2020-05-23 11:59

This is the number

This is the number 2^102589933

 LaurV 2020-05-23 13:34

[QUOTE=Glenio;546287]This is the number 2^102589933[/QUOTE]
This number can not be prime, as it is divisible by 2. Actually, you can divide it by 2 about a hundred million times, and you still get integers all along, which are still not prime, none of them is prime.

 kriesel 2020-05-23 13:56

[QUOTE=Glenio;546287]This is the number 2^102589933[/QUOTE]That number is composite (not prime) by definition. b[SUP]a[/SUP] for b>1, a>1, a and b integer, is composite; b is a factor. This may win the prize for most obviously NOT prime (which is public embarrassment). It has one prime factor and over a hundred million distinct composite factors 2[SUP]1[/SUP], 2[SUP]2[/SUP], 2[SUP]3[/SUP], ..., 2[SUP]102589932[/SUP].
[URL]https://www.mersenneforum.org/showpost.php?p=521665&postcount=3[/URL]
It also happens to have a superficial relationship to the largest known Mersenne prime, 2[SUP]82589933[/SUP]-1, whose exponent is 20M less.
See also, for the perfect record of predicting large primes,by various means, [URL]https://www.mersenneforum.org/showpost.php?p=512904&postcount=5[/URL]
Possibilities, more likely first: Inaccurate post lacking +-c, trolling, combination, computation error, something else, new prime discovery.

In the very unlikely event that it's a Mersenne prime discovery, verification should have quietly occurred without posting an exponent, then announcement via MRI Inc. press release. [URL]https://www.mersenneforum.org/showpost.php?p=490315&postcount=14[/URL]

 paulunderwood 2020-05-23 14:15

[QUOTE=kriesel;546292]That number is composite (not prime) by definition. b[SUP]a[/SUP] for b>1, a>1, a and b integer, is composite; b is a factor. This may win the prize for most obviously NOT prime.
[URL]https://www.mersenneforum.org/showpost.php?p=521665&postcount=3[/URL]
It also happens to have a superficial relationship to the largest known Mersenne prime, 2[SUP]82589933[/SUP]-1, whose exponent is 20M less.
See also, for the perfect record of predicting large primes,by various means, [url]https://www.mersenneforum.org/showpost.php?p=512904&postcount=5[/url][/QUOTE]

The "8" --> "10" in the exponent would be beyond expectation. It would take a day on a GPU you to dismiss this claim, assuming P-1 does not turn up a factor.

 kriesel 2020-05-23 14:28

[QUOTE=paulunderwood;546294]The "8" --> "10" in the exponent would be beyond expectation. It would take a day on a GPU [for] you to dismiss this claim, assuming P-1 does not turn up a factor.[/QUOTE]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.

 Glenio 2020-05-23 18:02

Prime Number

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.

 Uncwilly 2020-05-23 18:02

What software did you use to test it?
If you were using mprime or Prime95, email the save files to George Woltman.
If you used mlucas, contact Ernst Meyer with your save files.
Do you have any interim residues? Those would be helpful (we could have others test it and if there are mis-matches, we can see which 2 of 3 agree.)

 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.

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 ?

 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 ?

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.

 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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