A190799 Primes p=prime(i) such that prime(i+4)-prime(i)=20.

47, 83, 131, 137, 173, 191, 251, 257, 347, 419, 443, 557, 587, 593, 1013, 1019, 1031, 1049, 1217, 1301, 1427, 1433, 1439, 1979, 1997, 2069, 2267, 2531, 2657, 2687, 2693, 2699, 2711, 3251, 3299, 3539, 4007, 4211, 4241, 4253, 4643, 4931, 5003, 5099, 5399, 5501, 5861

Offset: 1

Author

Zak Seidov, May 20 2011

Keywords

• nonn

Comments

Consider sets of 5 consecutive primes with 4 different gaps 2,4,6,8.

From 4!=24 cases only 8 gap configurations are possible:

{2,4,6,8},{2,4,8,6},{2,6,4,8},{6,2,4,8},

{6,8,4,2},{8,4,2,6},{8,4,6,2},{8,6,4,2}.

Least sets of 5 consecutive primes with corresponding gap configurations are:

{{347,349,353,359,367},{2,4,6,8}}

{{1997,1999,2003,2011,2017},{2,4,8,6}}

{{10091,10093,10099,10103,10111},{2,6,4,8}}

{{8081,8087,8089,8093,8101},{6,2,4,8}}

{{83,89,97,101,103},{6,8,4,2}}

{{1439,1447,1451,1453,1459},{8,4,2,6}}

{{2531,2539,2543,2549,2551},{8,4,6,2}}

{{1979,1987,1993,1997,1999},{8,6,4,2}}.

Crossrefs

Only a small part of terms are also in A190792.

Programs

Mathematica

p = Prime[Range[1000]]; First /@ Select[Partition[p, 5, 1], Last[#] - First[#] == 20 &] (* T. D. Noe, May 23 2011 *)