A370453 Twin prime pair sums that equal a twin prime pair product plus 1 (divided by 36).

36, 144, 1764, 5184, 360000, 412164, 777924, 4536900, 5673924, 7225344, 12659364, 12830724, 20684304, 37601424, 56972304, 64160100, 81757764, 179506404, 194100624, 255104784, 309689604, 366339600, 461906064, 689062500, 689692644, 1191078144, 1495368900, 1538835984

Offset: 1

Author

Keith F. Lynch, Feb 18 2024

Keywords

• nonn

Comments

A twin prime pair (other than {3,5}) is always in the form {6m-1,6m+1}, so the product of the pair is always in the form 36*m^2-1 and a twin prime sum is always in the form 12m. As such, a twin prime sum can be one more than a twin prime product, but not vice versa, nor can a sum and product ever be equal.

{71,73} and {881,883} appear both as sums and as products.

Examples

			144 is a term because 71+73 = 144 and 11*13 = 143.
5184 is a term because 2591+2593 = 5184 and 71*73 = 5183.
		

Links

• Keith F. Lynch, Table of n, a(n) for n = 1..197

Crossrefs

Subset of A037072.

Cf. A152787.

Programs

Mathematica

With[{p = Select[Prime[Range[4200]], PrimeQ[# + 2] &]}, Select[p*(p + 2) + 1, And @@ PrimeQ[#/2 + {-1, 1}] &]] (* Amiram Eldar, Feb 19 2024 *)