A067377 Primes expressible as the sum of (at least two) consecutive primes in at least 1 way.

5, 17, 23, 31, 41, 53, 59, 67, 71, 83, 97, 101, 109, 127, 131, 139, 173, 181, 197, 199, 211, 223, 233, 251, 263, 269, 271, 281, 311, 331, 349, 353, 373, 379, 401, 421, 431, 439, 443, 449, 457, 463, 479, 487, 491, 499, 503, 523, 563, 587, 593, 607, 617, 631, 647, 659, 661, 677, 683, 691, 701, 719

Offset: 1

Author

Patrick De Geest, Feb 04 2002

Keywords

• nonn

Examples

			The prime 83, for example, is the sum of the five consecutive primes 11 + 13 + 17 + 19 + 23.
The prime 2011, for example, is the sum of the eleven consecutive primes 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211. - _Daniel Forgues_, Nov 03 2011
		

Links

• Hans Havermann, Table of n, a(n) for n = 1..34589
• Patrick De Geest, WONplate 122
• Hans Havermann, List of possible number of consecutive primes for n = 1..293768
• Carlos Rivera, Puzzle 46. Primes expressible as sum of consecutive primes in K ways, The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A050936, A067372-A067381, A307610.

Cf. A197227 (primes that are not the sum of consecutive primes).

Programs

Mathematica

p = {}; Do[a = Table[ Prime[i], {i, n, 150}]; l = Length[a]; k = 2; While[k < l + 1, b = Plus @@@ Partition[a, k]; k++; p = Append[ p, Select[ b, PrimeQ[ # ] &]]], {n, 1, 149}]; Take[ Union[ Flatten[p]], 70]
m=5!; lst={}; Do[p=Prime[a]; Do[p+=Prime[b]; If[PrimeQ[p]&&p<=Prime[m]*3+8,AppendTo[lst,p]],{b,a+1,m+2,1}],{a,m}]; Union[lst] (* Vladimir Joseph Stephan Orlovsky, Aug 15 2009 *)

Formula

Prime(n) such that A307610(n) > 1. - Ray Chandler, Sep 21 2023

Extensions

Offset changed to 1 by Hans Havermann, Oct 07 2018