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Catalan-Mersenne numbers
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Hi everybody,
I went through this forum looking for a thread talking about Catalan-Mersenne numbers, and I didn't find one.
I was wondering if the PrimeGrid project could be the place where we could calculate the C5 element of that Catalan sequence. C5 is equal to Mersenne number M170141183460469231731687303715884105728
I know this is a bit crazy because this number has about 646 millions digits...
But is it possible ? Is it mathematically relevant ? | |
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 Michael Goetz Volunteer moderator
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Joined: 21 Jan 10
Posts: 13804
ID: 53948
Credit: 345,369,032
RAC: 1,967
                              
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Hi everybody,
I went through this forum looking for a thread talking about Catalan-Mersenne numbers, and I didn't find one.
I was wondering if the PrimeGrid project could be the place where we could calculate the C5 element of that Catalan sequence. C5 is equal to Mersenne number M170141183460469231731687303715884105728
I know this is a bit crazy because this number has about 646 millions digits...
But is it possible ? Is it mathematically relevant ?
My understanding of the licensing of Prime95 -- and therefore of gwnum, which forms the basis of both LLR and PFGW -- prohibits anyone else from using the software on Mersenne numbers. That function is reserved to GIMPS itself.
We have no software that is not based on gwnum which can test the primality of C5, and although such software certainly exists, the best tool for the job is likely to b Prime95. I suggest, therefore, that you take your question over to the Mersenne forums, and ask there.
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My lucky number is 75898524288+1 | |
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Michael GoetzVolunteer moderator
Project administrator
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Joined: 21 Jan 10
Posts: 13804
ID: 53948
Credit: 345,369,032
RAC: 1,967
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I know this is a bit crazy because this number has about 646 millions digits...
But is it possible ? Is it mathematically relevant ?
Maybe I'm missing something, but I don't think C5 has 646 million digits.
According to the link you provided, C5 is 2170141183460469231731687303715884105728-1.
select format(170141183460469231731687303715884105728 * log10(2),0);
+--------------------------------------------------------------+
| format(170141183460469231731687303715884105728 * log10(2),0) |
+--------------------------------------------------------------+
| 51,217,599,719,369,680,000,000,000,000,000,000,000 |
+--------------------------------------------------------------+
It has 51e36 digits, or 51 trillion trillion trillion digits. 646 million digits is probably possible (ignoring the licensing problem) if you had a very powerful computer and a LOT of patience, but 51 trillion trillion trillion digits is laughably beyond what we can do.
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My lucky number is 75898524288+1 | |
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Michael is right. The number has 51,217,599,719,369,681,875,006,054,625,051,616,350 digits. Or about 51 undecillion digits (short scale).
Such a number cannot be tested.
One can trial factor. But check how far it has been done already.
Remember that any factor has the form:
2 * 170141183460469231731687303715884105727 * k + 1
for some positive integer k. The k that make this factor candidate expression a prime, are 57, 62, 194, 204, 249, 348, 369, 387, 390, . . ., cf. A057440.
/JeppeSN | |
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Message boards :
General discussion :
Catalan-Mersenne numbers |
