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 A007506 Primes p with property that p divides the sum of all primes <= p. (Formerly M1554) 9
 2, 5, 71, 369119, 415074643 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS No others < 29505444491. - Jud McCranie, Jul 08 2000 No other terms < 10^12. - Jon E. Schoenfield, Sep 11 2008 a(6), if it exists, is larger than 10^14. - Giovanni Resta, Jan 09 2014 Also primes p with property that p divides 1 plus the sum of all composites < p.  - Vicente Izquierdo Gomez, Aug 05 2014 REFERENCES J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 71, p. 25, Ellipses, Paris 2008. Harry L. Nelson, Prime Sums, J. Rec. Math., 14 (1981), 205-206. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS H. L. Nelson, Letter to the Editor re: Prime Sums, J. Recreational Mathematics 14.3 (1981-2), 205. (Annotated scanned copy) C. Rivera, Puzzle EXAMPLE 2 divides 2; 5 divides 2 + 3 + 5; 71 divides 2 + 3 + 5 + 7 + ... + 61 + 67 + 71; etc. MAPLE A007506:=proc(q)  local a, n; a:=0; for n from 1 to q do a:=a+ithprime(n); if gcd(ithprime(n), a)>1 then print(ithprime(n)); fi; od; end: A007506(10^10); # Paolo P. Lava, Mar 06 2013 MATHEMATICA sumOfPrimes = 0; Do[ sumOfPrimes += p;  If[ Divisible[ sumOfPrimes, p], Print[p]], {p, Prime /@ Range[23000000]}]  (* Jean-François Alcover, Oct 22 2012 *) Transpose[Module[{nn=23000000, pr}, pr=Prime[Range[nn]]; Select[Thread[ {Accumulate[ pr], pr}], Divisible[#[[1]], #[[2]]]&]]][[2]] (* Harvey P. Dale, Feb 09 2013 *) PROG (PARI) s=0; forprime(p=2, 1e9, s+=p; if(s%p==0, print1(p", "))) \\ Charles R Greathouse IV, Jul 22 2013 CROSSREFS Cf. A024011, A028581, A028582. Sequence in context: A013045 A290864 A309366 * A042693 A172037 A301993 Adjacent sequences:  A007503 A007504 A007505 * A007507 A007508 A007509 KEYWORD nonn,nice,hard,more AUTHOR EXTENSIONS Example corrected by Harvey P. Dale, Feb 09 2013 STATUS approved

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Last modified September 17 04:03 EDT 2019. Contains 327119 sequences. (Running on oeis4.)