A163111
Prime numbers with gaps larger than 18 towards both neighboring primes.
Original entry on oeis.org
3967, 11027, 11657, 14107, 16033, 16787, 18013, 18617, 18637, 18839, 19661, 21247, 23719, 24281, 24571, 29101, 30367, 31357, 32749, 33247, 33679, 33997, 35201, 36037, 37747, 38501, 40063, 40387, 42533, 42611, 43691, 43913, 44417, 46957
Offset: 1
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lst={};Do[p=Prime[n];If[ !PrimeQ[p-2]&&!PrimeQ[p+2]&&!PrimeQ[p-4]&&!PrimeQ[p+4]&&!PrimeQ[p-6]&&!PrimeQ[p+6]&& !PrimeQ[p-8]&&!PrimeQ[p+8]&&!PrimeQ[p-10]&&!PrimeQ[p+10]&&!PrimeQ[p-12]&&!PrimeQ[p+12]&&!PrimeQ[p-14]&&!PrimeQ[p+14]&&!PrimeQ[p-16]&&!PrimeQ[p+16]&&!PrimeQ[p-18]&&!PrimeQ[p+18], AppendTo[lst,p]],{n,8!}];lst
Select[Partition[Prime[Range[5000]],3,1],Min[Differences[#]]>18&][[All,2]] (* Harvey P. Dale, Jul 08 2021 *)
A163112
Prime numbers with gaps larger than 20 towards both neighboring primes.
Original entry on oeis.org
16033, 16787, 18013, 23719, 24281, 29101, 32749, 33247, 33679, 33997, 37747, 38501, 40063, 40387, 42533, 42611, 44417, 46957, 51109, 51383, 53479, 54217, 55291, 55763, 56333, 56569, 58271, 58511, 58831, 59833, 61441, 61781, 62273, 66137, 66271, 69593, 69623
Offset: 1
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p := 2; q := 3; r := 3; for n from 2 to 15000 do if q-p > 20 and r-q > 20 then printf("%d,",q) ; fi; p := q; q := r; r := nextprime(r) ; od: # R. J. Mathar, Jul 27 2009
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Select[Partition[Prime[Range[7000]],3,1],Min[Differences[#]]>20&] [[All, 2]] (* Harvey P. Dale, Mar 16 2017 *)
A167839
Five-times-isolated primes: primes p such that none of (p-10,p-8,p-6,p-4,p-2,p+2,p+4,p+6,p+8,p+10) are prime.
Original entry on oeis.org
2, 211, 1511, 1847, 2179, 2503, 2579, 2633, 2819, 2939, 3137, 3271, 3433, 3659, 3967, 3989, 4111, 4177, 4409, 4621, 4691, 4703, 4831, 4889, 5039, 5209, 5261, 5623, 5939, 5953, 6619, 6637, 6883, 7057, 7283, 7369, 7393, 7433, 7621, 7741, 7841, 7853, 7963
Offset: 1
a(1)=2 (-8,-6,-4,-2,0,4,6,8,10,12 are nonprimes); a(2)=211 (201,203,205,207,209,213,215,217,219,221 are nonprimes).
1831 was incorrect. 3967 appeared twice. 4703, 5209 and 5261 were missing. Added more terms
Dmitry Kamenetsky, Nov 30 2009
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