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A repository of say 13 digit prime, 15 digit primes etc.

Regret
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Onkar Singh Gujral
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  • Wikipedia , there are lot of sequences, just find a sequence which increases fast enough, you can easily make it to 13 digit or 15 digit, but various of them might be omitted the kind of sequence depend upon how many you require. – Someone May 07 '15 at 06:37
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    (1) Download Pari/GP from http://pari.math.u-bordeaux.fr/. (2) run forprime(n=10^13,10^14,print(n)). Enjoy your big list of primes. Change the bounds as desired. There is lots of software that can do this of course -- primesieve from http://primesieve.org/ is another good source. The latter especially will generate them much faster than you could download a list (unless you have an Apple // with fast internet). – DanaJ May 07 '15 at 06:47
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    BTW FYI the largest known prime number is

    $2^{257885161}-1$

    ** Here are some links:**

    https://primes.utm.edu/lists/small/millions/

    http://www.bigprimes.net/archive/prime/

    Wikipedia:

    http://en.wikipedia.org/wiki/List_of_prime_numbers

     – NeilRoy May 07 '15 at 06:56
  • Thank you very much for that Prime Pages link, @NeilRoy. Chris Caldwell writes: "For about ten years I resisted placing large files of primes on the Prime Pages because it can be a waste of bandwidth. Programs can find them far faster than they can be downloaded. So instead I linked to others who had such files. But these sites kept disappearing and the requests for the primes did not. So here they are. Besides, downloading primes is a better use of bandwidth then much of the downloading done on the Internet." –  May 13 '15 at 15:40
  • @AlonsodelArte Good quote and you are welcome! – NeilRoy May 13 '15 at 15:46

2 Answers2

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There are $308,457,624,821$ 13 digit primes and $26,639,628,671,867$ 15 digit primes. I suppose somebody might waste some terabytes with lists of all of them, but they'll take a while to download..

EDIT: Google did not find a match for the $13$ digit prime 4257452468389. So maybe there is no Google-accessible list of all $13$ digit primes on the internet. Some time after I post this, I imagine Google will get a hit, namely this posting.

Robert Israel
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    Perhaps they are stored as differences. You could store all the 13 digit primes in ~300GB (simple method: store (gap-2)/2 as a byte with escape code). It'd be so much easier to just download and run primesieve, Pari/GP, Perl/ntheory, or some other tool. – DanaJ May 07 '15 at 18:03
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    I wonder how efficiently zip would compress the file. – Robert Israel May 07 '15 at 19:42
  • Looking at the first 36M 13 digit primes as a text file, gzip -9 and zip use about 2.7 bytes per prime. bzip2 -9 is 3.1 bytes/prime. I didn't test xz. The gap difference file would be basically no compression, though one could get slightly better results using things like rice or exponential gamma coding. – DanaJ May 07 '15 at 21:02
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This website here provides a list of many known prime numbers, and You can actually find very large primes there, including 13,15 digits primes, and even way more than that

alkabary
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    All known prime numbers? I don't think so. For example, I doubt that $3125250912230709951372256510072774348164206451981118444862954305561681091773335180100000000000000000537$ is on the list (well, maybe it wasn't known five minutes ago, but it is now). – Robert Israel May 07 '15 at 06:42
  • Most of them :D – alkabary May 07 '15 at 06:48
  • I think "...lists of many prime numbers..." is more accurate. "all known" is absurd, and "most known primes" isn't true either. – DanaJ May 07 '15 at 06:52
  • Ok , i will edit that – alkabary May 07 '15 at 07:00