

A124588


Primes p such that q  p <= 2, where q is the next prime after p.


7



2, 3, 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 461, 521, 569, 599, 617, 641, 659, 809, 821, 827, 857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1277, 1289, 1301, 1319, 1427, 1451, 1481, 1487, 1607
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OFFSET

1,1


COMMENTS

Consists of 2 together with the lower members of twin primes, A001359. See the latter entry for references.
"Assuming certain (admittedly difficult) conjectures on the distribution of primes in arithmetic progressions, [GoldstonPintzYildirim] prove the existence of infinitely many prime pairs that differ at most by 16."  Soundararajan
The prime differences of 2 primes (without repetition).  JuriStepan Gerasimov, Jun 01 2010, Jun 08 2010
Numbers k such that sigma(k*(k+2)) = (k+1)*(k+3).  Wesley Ivan Hurt, May 08 2022


LINKS



MATHEMATICA

Transpose[Select[Partition[Prime[Range[300]], 2, 1], #[[2]]#[[1]]<3&]] [[1]] (* Harvey P. Dale, Feb 11 2015 *)


PROG

(PARI) twinl(n) = { c=0; x=1; while(c<n, if(isprime(prime(x)+2), c++); x++; ); return(prime(x1)) }
print1(2", "); (for(x=1, 200, print1(twinl(x)", "))) \\ Cino Hilliard, Mar 29 2008


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



