The Biggest Prime

February 8, 2013

It has been widely reported that a new “biggest prime” was found two weeks ago. The prime, which has 17,425,170 digits, is:

257,885,161 − 1

Your task is to write a program that displays all seventeen million digits of the biggest prime. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.


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12 Responses to “The Biggest Prime”

  1. danaj said

    From the command line:

    perl -E 'use bigint lib=>"GMP"; say 2**57_885_161-1'

    redirect to a file if you’d like. Produces 17,425,171 digits in under 5 seconds on my machine.

    Using the Pari backend requires raising the Pari stacksize — I didn’t try it. Using the default Calc backend is quite slow as expected with very big numbers — I killed it after 7 minutes.

  2. Justin said

    Fabrice Bellard’s solution to a smaller Mersene can be found here :

  3. Globules said


    main = print $ 2^57885161-1
  4. Paul said

    The first attempt using Python 2.7 failed. It is no problem to make the prime, but printing it (or converting it to a string) takes more than 2 hours (and maybe never finishes). Using the gmpy library the time taken is 22 secs. It creates a file of about 17 MB.

    import gmpy
    out = open("bigprime.txt", "w")
    n = gmpy.mpz(2 ** 57885161 - 1)
  5. […] ¿cuáles son todas las cifras del primo 48 de Mersenne? En erl sitio Programming Praxis se reta a los lectores (programadores) a que generen los 17 millones de dígitos. Un programa […]

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  7. bitchef said

    I had to use the GMP C Library.
    There exists a function to specifically do this sort of thing. Here is my code in C :

    #include <gmp.h>
    int main(){    
        mpz_t one;
        mpz_t op1;
        long op2 = 57885161 ;
        mpz_t temp;
        mpz_t result;
        mpz_set_ui(op1, 1);
        mpz_set_ui(one, 1);
        mpz_mul_2exp(temp , op1, op2);
        mpz_sub(result , temp, one);
        gmp_printf("The biggest prime number  is \n %Zd\n " , result );

    Redirecting the big prime to a file produces a 16.6 Mb file on my machine. It runs in under 3 seconds on my old laptop with a Pentium 4 processor.

  8. kbob said

    I decided to print it in hex. (-:

    >>> def pmx(n): return '137'[:n % 4][-1:] + 'f' * (n / 4)
    >>> print pmx(57885161)
  9. razvan said

    What I found out today is that Standard ML’s big integer library appears to be horrifically slow.
    The code is:
    Control.Print.intinfDepth := 17500000;
    IntInf.pow (LargeInt.fromInt 2, 57885161) – 1;
    It’s still running after about 5 hours.

  10. […] trying to solve the biggest prime programming praxis problem in C#. The problem is simple, print out or write to file the number: […]

  11. Christo said

    Globules said
    February 9, 2013 at 8:07 AM

    Haskell: 1 main = print $ 2^57885161-1

    581887266232246442….. Wrong!!

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