A059767 Initial (unsafe) primes of Cunningham chains of first type with length exactly 7.

1122659, 2164229, 2329469, 10257809, 10309889, 12314699, 14030309, 14145539, 23103659, 24176129, 28843649, 37088729, 42389519, 49160099, 50785439, 62800169, 68718059, 88174049, 95831189, 105388169, 121255889, 138140729, 155439419, 159938459, 173285999

Offset

1,1

Comments

Special primes from A059453.

References

David Wells, The Penguin Dictionary of Curious and Interesting Numbers, p. 178 (Rev. ed. 1997).

Links

Table of n, a(n) for n=1..25.

Formula

p primes, (2^k)*p+(2^k)-1 is prime too for k=0, 1, 2, 3, 4, 5, 6 and is composite for k=-1 and k=7.

Example

C7 prime chain is generated from prime a(10)=24176129 with 2p+1 iteration: 24176129, 48352259, 96704519, 193409039, 386818079, 773636159, 1547272319, 3094544639.

Mathematica

Transpose[Select[{#, Length[NestWhileList[2#+1&, #, PrimeQ]]-1}&/@ Prime[Range[PrimePi[24177000]]], #[[2]]>6&]][[1]]
Select[Prime[Range[10^6]], PrimeQ[a1=2*#+1]&&PrimeQ[a2=2*a1+1]&&PrimeQ[a3=2*a2+1]&&PrimeQ[a4=2*a3+1]&&PrimeQ[a5=2*a4+1]&&PrimeQ[a6=2*a5+1] &] (* Vladimir Joseph Stephan Orlovsky, May 01 2008 *)

Prog

(PARI) is(n)=n%30==29 && isprime(n) && isprime(2*n+1) && isprime(4*n+3) && isprime(8*n+7) && isprime(16*n+15) && isprime(32*n+31) && isprime(64*n+63) && !isprime(n\2) && !isprime(128*n+127) \\ Charles R Greathouse IV, Dec 01 2016

Crossrefs

Cf. A005384, A005385, A005602, A007700, A023272, A023302, A023330, A059452, A059453, A059454, A059455.

Sequence in context: A059121 A116175 A278932 * A069583 A109209 A340229

Adjacent sequences: A059764 A059765 A059766 * A059768 A059769 A059770

Keyword

nonn

Author

Labos Elemer, Feb 21 2001

Extensions

Corrected and extended by Harvey P. Dale, Jul 10 2002

More terms from Vladimir Joseph Stephan Orlovsky, Jan 17 2009

Corrected by John Cerkan, Nov 30 2016

Status

approved