A080172 Final digit of n-th Mersenne prime A000668(n).

3, 7, 1, 7, 1, 1, 7, 7, 1, 1, 7, 7, 1, 7, 7, 7, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 7, 7, 1, 7, 7, 1, 7, 1, 1, 1, 1, 1, 7, 7, 7, 1, 1, 7, 1, 1, 1

Offset: 1

Author

Mark Dowdeswell, Feb 04 2003

Keywords

• base
• more
• nonn

Comments

Distribution of final digit for Mersenne primes appears (naturally) to be different from distribution for regular primes. Unconfirmed 49th, 50th and 51st digits in sequence are 1, 1, 1 (awaiting confirmation of 49th, 50th and 51st Mersenne primes).

References

• G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 16.

Links

• Great Internet Mersenne Prime Search (GIMPS), Distributed Computing Projects
• Mersenne Primes, History, Theorems and Lists

Crossrefs

Cf. A000668, A007652, A080173.

Programs

Maple

(Maple code from N. J. A. Sloane) # let s1 := list of terms in A000043
f:=n->if n mod 4 = 0 then 4 else n mod 4; fi; map(x->2^f(x)-1,s1);

Mathematica

Mod[2^MersennePrimeExponent[Range[48]]-1,10] (* Harvey P. Dale, Aug 09 2023; updated by Mark Dowdeswell, Sep 16 2024 *)

Extensions

Updated by N. J. A. Sloane, Apr 01 2008

a(40)-a(47) from Ivan Panchenko, Apr 11 2018

a(48) from Mark Dowdeswell, Sep 16 2024