A374613 Prime numbers p with the property that neither of 2*(p+next prime to p)+/-1 is prime.

29, 71, 73, 79, 83, 127, 131, 137, 167, 173, 193, 197, 211, 223, 229, 233, 239, 251, 269, 331, 347, 349, 373, 419, 421, 431, 433, 439, 457, 467, 487, 503, 509, 541, 563, 577, 587, 619, 641, 647, 653, 659, 661, 691, 719, 727, 733, 743, 751, 797, 809, 811, 821, 829, 839, 853, 859, 863, 887

Offset: 1

Author

Marcin Barylski, Jul 14 2024

Keywords

• nonn

Comments

Conjecture: this sequence is infinite.

Examples

			2 is not a term because 2*(2+3)+1=11 is a prime.
5 is not a term because 2*(5+7)-1=23 is a prime.
29 is a term because neither 2(29+31)+1 nor 2(29+31)-1 is a prime.
		

Programs

Mathematica

Prime[Select[Range[155], !PrimeQ[2(Prime[#]+Prime[#+1])-1] && !PrimeQ[2(Prime[#]+Prime[#+1])+1]&]] (* Stefano Spezia, Jul 15 2024 *)