A089628 Smallest member of a pair of consecutive twin prime pairs that have no primes between them.

3, 5, 11, 101, 137, 179, 191, 419, 809, 821, 1019, 1049, 1481, 1871, 1931, 2081, 2111, 2969, 3251, 3359, 3371, 3461, 4217, 4229, 4259, 5009, 5651, 5867, 6689, 6761, 6779, 6947, 7331, 7547, 8219, 8969, 9419, 9431, 9437, 10007, 11057, 11159, 11699, 12239

Offset: 3

Author

Cino Hilliard, Jan 01 2004

Keywords

• easy
• nonn

Comments

Run the PARI script savetwins(100000) or so to build the twinprime array of lower bounds before you run the main script.

Except for first term, same as A053778. - David Wasserman, Feb 22 2006

Examples

			Twin prime pairs 5,7 and 11,13 contain only the composite numbers 6,7,8,9,10 between them. So 5 is in the table. 11,13 and 17,19 have no primes between.
11 is in the table. 41,43 and 59,61 have primes 47 and 53 between then so 41 is not listed.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 3..1000

Programs

Mathematica

Join[{3},Select[Partition[Prime[Range[1500]],4,1],#[[4]]-#[[3]]==#[[2]]- #[[1]] == 2&][[All,1]]] (* Harvey P. Dale, Dec 15 2018 *)

PARI

\save as twinpr.gp pbetweentw(n) = { forstep(x1=1,n,2, c=0; t1 = twin[x1]; t2 = twin[x1+2]; for(y=t1+3,t2-1, if(isprime(y),c++) ); if(c==0,print1(t1",")) ) } savetwins(n) = build a table of twin prime I want to upload a supporting file to store with the OEIS and add a link to it.lower bounds { twin = vector(n); c=1; forprime(x=3,n, if(isprime(x+2), twin[c]=x; c++; ) ) }