91–100 of 115 posts
tl;dr The 50th Mersenne prime was just found by a volunteer of the GIMPS (Great Internet Mersenne Prime Search) project. It is 2^77,232,917-1 and has 23,249,425 digits. Mersenne primes are extremely rare and are always of the form 2^p-1 for some positive integer p. The first four Mersenne primes are 3, 7, 31, and 127.
Also, p is prime.
Curious: can bitcoin mining rigs be modified for BOINC projects (GIMPS, Seti@Home, etc.)? If yes, than I might invest in some rigs and modify them to run BOINC. Yes, I'm weird: I prefer to do computation for BOINC than for bitcoin. :-)
nowadays bitcoin mining rigs use ASICs that are optimized for the task, so I don't think that would be a good idea. on a general purpose system you can use GPUs and BOINC with SETI, not sure about GIMPS.
I do have some PC systems but they are shared among family members, making it difficult to run BOINC as a background task without interfering with their work.
I'll look at low-cost systems, like the Raspberry Pi, to see if I can use them as dedicated BOINC boxes instead.
Earlier quoted context omitted.
> so I didn't know this, but got curious about how many known prime there are This isn't the exact question you're asking, but we actually know the distribution of prime numbers, which allows us to calculate the (approximate) number of primes that are less than or equal to an arbitrary value. Since the largest prime discovered is 2^(277,232,917-1), that means that the number of primes less than or equal to that numbe…
Nit: the largest prime discovered is 2^(277,232,917)-1 not 2^(277,232,917-1)
(2^77,232,917)-1
Earlier quoted context omitted.
RSA encryption keys uses the product of two large primes, where each prime is many digits long. So many new primes are "discovered" every day.
Interestingly, those primes' primality is normally proven statistically rather than deductively. This is not really a practical issue for people using RSA, but could be a philosophical issue for someone interested in the question of how many different numbers' primality has been proven by humanity.
Earlier quoted context omitted.
Nit: the largest prime discovered is 2^(277,232,917)-1 not 2^(277,232,917-1)
If you read the article, it's actually: (2^77,232,917)-1
Earlier quoted context omitted.
If you read the article, it's actually: (2^77,232,917)-1
Not sure if this was a serious comment, but if it was: due to operator precedence in mathematics, the expressions (2^77,232,917)-1, 2^(77,232,917)-1, and 2^77,232,917-1 are identically evaluated, with the parentheses only used to aid the human eye. This in contrast to 2^(77,232,917-1), which is 2^77,232,916 and is a very different number indeed.
Earlier quoted context omitted.
Nit: the largest prime discovered is 2^(277,232,917)-1 not 2^(277,232,917-1)
If you read the article, it's actually: (2^77,232,917)-1
2 ⁷⁷ ²³² ⁹¹⁷ − 1
not
2 ⁷⁷ ²³² ⁹¹⁷ ⁻ ¹
There, no more ambiguity.
(Now I’m waiting for someone to jump on me to correct anything subtle.)
[Ah, I see, the parentheses were indeed a red herring. Ah well; let the superscripts remain.]
TIL I work at the same company as the discoverer of the 50th known Mersenne Prime. I know at least one sysadmin who used GIMPS as a burn-in program for new servers.....
Earlier quoted context omitted.
If you read the article, it's actually: (2^77,232,917)-1
Not sure if this was a serious comment, but if it was: due to operator precedence in mathematics, the expressions (2^77,232,917)-1, 2^(77,232,917)-1, and 2^77,232,917-1 are identically evaluated, with the parentheses only used to aid the human eye. This in contrast to 2^(77,232,917-1), which is 2^77,232,916 and is a very different number indeed.