A131499 Primes p such that nextprime(p)=p+4 and previousprime(p)

37, 67, 79, 97, 127, 163, 223, 277, 307, 379, 397, 439, 457, 487, 499, 613, 673, 739, 757, 769, 853, 877, 907, 937, 967, 1009, 1087, 1213, 1297, 1423, 1447, 1549, 1567, 1579, 1597, 1663, 1693, 1783, 1867, 1993, 2137, 2203, 2293, 2347, 2377, 2389, 2437

Offset: 1

Author

Zak Seidov, Aug 12 2007

Keywords

• nonn

Comments

Or a=p+1, b=p+2 and c=p+3 are composite triples: a,b,c are composite while a-1 and c+1 are not. There are no composite twins and composite singles are interprimes of twin primes. All numbers are congruent to 1 mod 6 (and not congruent to 1 mod 10). First differences divided by 6 are: 5,2,3,5,6,10,9,5,12,3,7,3,5,2,19,10,11,3,2,14,4,5,5,5,7,13,21,14,21,4,17,...

Examples

			a(1)=37 because nextprime(37)=41=37+4 and previousprime(37)=31<37-4,
a(2)=67 because nextprime(67)=71=67+4 and previousprime(67)=61<67-4.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Programs

Mathematica

p1000=Prime[Range[1000]]; c=0; Do[p=p1000[[i]]; If[p-p1000[[i-1]]>4&&p1000[[i+1]]==4+p, c++; a[c]=p],{i,2,999}]; Table[a[i],{i,c}]
Select[Prime[Range[400]],NextPrime[#]-#==4&&#-NextPrime[#,-1]>4&] (* Harvey P. Dale, Jul 16 2012 *)