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

1,1

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.

Links

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

Example

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

Mathematica

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

Crossrefs

Subset of A037072.

Cf. A152787.

Sequence in context: A154711 A162992 A037072 * A076432 A003848 A203753

Adjacent sequences: A370450 A370451 A370452 * A370454 A370455 A370456

Keyword

nonn

Author

Keith F. Lynch, Feb 18 2024

Status

approved