A233002 Primes p > 3 such that p+6*k is composite for all k from 1 to 100.

1917214927, 1917281213, 2540118761, 2560601663, 2977271357, 3059526377, 3868900621, 4211712397, 4237592851, 4823026847, 4899889741, 5120099581, 5719551907, 5822257871, 5880593053, 6362295487

Offset

1,1

Comments

In some sense this is the opposite to the problem of (consecutive) primes in the arithmetic progression PAP or CPAP.

Note that in many cases p + 6*k are composite for k = 1..m with m > 100.

Maximal found value of m = 148 for a(615) = 50100585793 = prime(2123734960).

Is it possible to find primes p giving, say, thousand composites p+6*k, k = 1..1000 or even more?

Of course we exclude the cases p = 2 and 3 as they give an infinite number of composites of the form p + 6*k.

Links

Zak Seidov, Table of n, a(n) for n = 1..2035 (all terms up to 10^11)

Example

1917214927 + {6, 12, 18, 24, ..., 600} are all composite.

Mathematica

Select[Prime[Range[3*10^8]], AllTrue[#+6*Range[100], CompositeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 25 2018 *)

Crossrefs

Sequence in context: A103752 A105383 A339251 * A165075 A034252 A016931

Adjacent sequences: A232999 A233000 A233001 * A233003 A233004 A233005

Keyword

nonn,more

Author

Zak Seidov, Dec 03 2013

Extensions

First two terms prepended by Harvey P. Dale, Mar 25 2018

2, 3 removed again by Georg Fischer, Jan 20 2019

Status

approved