

A087382


Twin prime indices of primes forming a twin prime member.


0



3, 5, 7, 11, 13, 17, 29, 41, 43, 61, 109, 149, 179, 191, 269, 313, 347, 431, 461, 463, 601, 617, 643, 659, 829, 859, 1031, 1033, 1051, 1231, 1279, 1321, 1619, 1621, 1879, 1931, 1949, 1999, 2029, 2309, 2311, 2341, 2383, 2711, 2789, 2791, 2801, 3253, 3299, 3329
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

3,1


COMMENTS

It is interesting that these primes occur rather frequently early on but gradually diminish as the iterations increase. Some ratios of count of twin primes p and the occurrence of prime(p) also a twin prime is as follows. Index< Ratio 1000 .74 10000 .48 100000 .39 1000000 .35 Looks like it is approaching a limit.


LINKS



EXAMPLE

The 29th prime,109,is also a twin prime paired with the prime 107.


PROG

(PARI) twips(n) = { c1=0; c2=0; forprime(x=3, n, if(isprime(x+2), c1++); x1=prime(x); if(isprime(x2)  isprime(x+2), if(isprime(x12)  isprime(x1+2), print1(x", "); c2++; ) ) ); print(); print(c2/c1+.0) }


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



