A193864 Decimal expansion of 2^43112609 - 1, the 47th Mersenne prime A000668(47).

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

Offset: 12978189

Author

Kausthub Gudipati, Aug 07 2011

Keywords

• nonn
• cons
• fini

Comments

This number is very large, containing 12978189 digits. Edson Smith discovered this prime number on August 26, 2008 within the GIMPS framework. Landon Curt Noll calculated the decimal expansion of this prime number. It is a Mersenne prime.

This 47th Mersenne prime (cf. A000043) is remarkable since it was found before two smaller Mersenne primes, one in the following month (September 2008) and another one in April 2009. It remained the largest known prime until January 2013, when the 48th known Mersenne prime was found. - M. F. Hasler, May 22 2014

Examples

			316470269330255923143453723949(...12978129 digits omitted...)887478265780022181166697152511
		

Links

• GIMPS, List of Known Mersenne Prime Numbers
• OEIS Wiki, Mersenne primes (with a list of similar sequences)

Crossrefs

Cf. A000043 (main entry), A000668, A028335 (lengths).

Programs

Mathematica

IntegerDigits[2^43112609 - 1][[1 ;; 105]] (* T. D. Noe, Aug 09 2011 *)

PARI

A193864_list(Nmax)={default(realprecision,Nmax+5);digits(10^frac(43112609*log(2)/log(10))\.1^Nmax)} \\ Use digits(x)=eval(Vec(Str(x))) in older PARI versions. - M. F. Hasler, Mar 04 2012, updated May 22 2014

PARI

write("a193864.txt", 2^43112609 - 1) \\ Georg Fischer, Mar 19 2019

Formula

2^43112609 - 1.

Extensions

Name changed by Georg Fischer, Mar 19 2019