A133802 Even numbers which are not the sum of a pair of cousin primes.

2, 4, 8, 12, 68, 72, 76, 278, 282, 286, 638, 642, 644, 648, 652, 908, 912, 916, 1058, 1062, 1066, 1328, 1332, 1336, 1418, 1422, 2114, 2118, 2122, 2294, 2298, 2302, 2528, 2532, 2536, 2948, 2952

Offset: 1

Author

Donovan Johnson, Jan 06 2008

Keywords

• nonn

Comments

No other n < 10^9. Conjectured to be complete.

Examples

			The cousin primes < 100 are 3, 7, 11, 13, 17, 19, 23, 37, 41, 43, 47, 67, 71, 79, 83, 97. 76 is in the sequence because no combination of any two numbers from the set just enumerated can be summed to make 76.
		

References

• D. Wells, Prime Numbers: The Most Mysterious Figures in Math. John Wiley & Sons, Inc., Hoboken, New Jersey, page 33.

Links

• Eric Weisstein's World of Mathematics, Cousin Primes.
• Marek Wolf, On the Twin and Cousin Primes, (1996) IFTU Wr 909/96.

Crossrefs

Cf. A023200, A046132, A007534.

Programs

Mathematica

Lim=10^4;cp1=Select[Range[Lim], PrimeQ[#] && PrimeQ[# + 4] &] ;cp=Union[Join[cp1,cp1+4]];sms=Total/@Tuples[cp,2];en=Range[2,Lim,2];Complement[en,sms] (* James C. McMahon, Mar 30 2025 *)