login
Decimal expansion of Mersenne prime 2^82589933 - 1.
2

%I #31 Apr 05 2024 16:53:21

%S 1,4,8,8,9,4,4,4,5,7,4,2,0,4,1,3,2,5,5,4,7,8,0,6,4,5,8,4,7,2,3,9,7,9,

%T 1,6,6,0,3,0,2,6,2,7,3,9,9,2,7,9,5,3,2,4,1,8,5,2,7,1,2,8,9,4,2,5,2,1,

%U 3,2,3,9,3,6,1,0,6,4,4,7,5,3,1,0,3,0,9

%N Decimal expansion of Mersenne prime 2^82589933 - 1.

%C This prime has 24862048 decimal digits and was found by Patrick Laroche with GIMPS on Dec 07 2018.

%H OEIS Wiki, <a href="/wiki/Mersenne_primes">Mersenne primes</a> (with a list of similar sequences)

%H Mersenne.ca, <a href="https://www.mersenne.ca/exponent/82589933">Link to the record prime:</a> M82589933

%e Prime starts with 14889444574204132554780645847...

%e and ends in ...66457823695074037951210325217902591

%t IntegerDigits[2^82589933 - 1][[;;100]] (* _Paolo Xausa_, Apr 05 2024 *)

%o (PARI) list(Nmax) = {localprec(Nmax+5); digits(10^frac(82589933*log(2)/log(10))\.1^Nmax)}

%o list(200) \\ print initial 200 digits

%o (Python)

%o f = open("M82589933.txt", "a")

%o f.write(str(pow(2,82589933)-1))

%o f.close() # _Karl-Heinz Hofmann_, Jun 05 2021

%o (Python)

%o from gmpy2 import mpz

%o def A344984(n): return int((mpz(2)**82589933-1)//mpz(10)**(49724095-n) % 10) # _Chai Wah Wu_, Jun 07 2021

%Y Cf. decimal expansions of Mersenne primes: A169681 (M127), A169685 (M521), A204063 (M607), A248931 (M1279), A248932 (M2203), A248933 (M2281), A248934 (M3217), A248935 (M4253), A248936 (M4423), A275977 (M9689), A275979 (M9941), A275980 (M11213), A275981 (M19937), A275982 (M21701), A275983 (M23209), A275984 (M44497), A089065 (M13466917), A089578 (M20996011), A117853 (M30402457), A193864 (M43112609), A267875 (M74207281), A344983 (M77232917).

%K nonn,cons,fini

%O 24862048,2

%A _Felix Fröhlich_, Jun 04 2021