|
Search: id:A059767
|
|
|
| A059767 |
|
Initial (unsafe) primes of Cunningham chains of first type with length exactly 7. |
|
+0
1
|
|
| 1122659, 2164229, 2329469, 10257809, 10309889, 12314699, 14030309, 14145539, 19099919, 23103659, 24176129
(list; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
Special primes from A059453.
|
|
REFERENCES
|
David Wells, The Penguin Dictionary of Curious and Interesting Numbers, p. 178 (Rev. ed. 1997).
|
|
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] &] (from Vladimir Orlovsky (4vladimir(AT)gmail.com), May 01 2008)
|
|
CROSSREFS
|
Cf. A023272, A023302, A023330, A005602, A007700 A005384, A005385, A059452-A059455.
Sequence in context: A038449 A059121 A116175 this_sequence A069583 A109209 A100365
Adjacent sequences: A059764 A059765 A059766 this_sequence A059768 A059769 A059770
|
|
KEYWORD
|
more,nonn
|
|
AUTHOR
|
Labos E. (labos(AT)ana.sote.hu), Feb 21 2001
|
|
EXTENSIONS
|
Corrected and extended by Harvey P. Dale (hpd1(AT)nyu.edu), Jul 10 2002
|
|
|
Search completed in 0.002 seconds
|
