A088250 a(n) is the smallest number k such that r*k + 1 is prime for all r = 1 to n.

1, 1, 2, 330, 10830, 25410, 512820, 512820, 12960606120, 434491727670, 1893245380950, 71023095613470, 878232256181280, 11429352906540438870

Offset: 1

Author

Amarnath Murthy, Sep 26 2003

Keywords

• nonn
• more

Comments

Conjectures: (1) Sequence is infinite. (2) For every n there are infinitely many arithmetic progressions with n successive primes.

Both conjectures follow from Dickson's conjecture. [Charles R Greathouse IV, Mar 14 2011]

Examples

			a(11) = 1893245380950 because all eleven numbers 1*1893245380950 + 1, 2*1893245380950 + 1, 3*1893245380950 + 1, ..., 10*1893245380950 + 1 & 11*1893245380950 + 1 are prime and 1893245380950 is the smallest number with such property.
		

Links

• Carlos Rivera, Puzzle 379. SG primes and its prime average, The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A088251, A088252, A088651, A125838, A125839.

Programs

Mathematica

a[n_] := Block[{k = If[n < 4, 1, 6], s}, s = k; While[! AllTrue[k Range[n] + 1, PrimeQ], k += s]; k]; Array[a, 8] (* Giovanni Resta, Mar 31 2017 *)

Extensions

Edited by Don Reble, Sep 29 2003

Entry revised by N. J. A. Sloane, Jan 05 2007

a(14) from Giovanni Resta, Mar 31 2017