A128469 Numbers of the form 30k+29 or possible lower bounds of twin primes pairs ending in 9.

29, 59, 89, 119, 149, 179, 209, 239, 269, 299, 329, 359, 389, 419, 449, 479, 509, 539, 569, 599, 629, 659, 689, 719, 749, 779, 809, 839, 869, 899, 929, 959, 989, 1019, 1049, 1079, 1109, 1139, 1169, 1199, 1229, 1259, 1289, 1319, 1349, 1379, 1409, 1439, 1469

Offset: 1

Author

Cino Hilliard, May 05 2007

Keywords

• easy
• nonn

Comments

For a 30k+r "wheel", r = 11,17,29 are the only possible values that can form a a lower twin prime pair. The 30k+r wheel gives the recurrence 1, 7,11,13,17,19,23,29 31,37,41,43,47,49,53,59 .. which is frequently used in prime number sieves to skip multiples of 2,3,5. The fact that adding 2 to 30k+1,7,13,19,23 will gives us a multiple of 3 or 5, precludes these numbers from being a lower member of a twin prime pair. This leaves us with r = 11,17,29 as the only possible cases to form a lower bound of a twin prime pair. The lower bound of twin prime pairs can only end in 1,7 or 9 since adding 2 to primes ending in 3 become multiples of 5.

Of the first 10000 terms of this sequence, only 988 are lower primes of a twin prime pair. [Harvey P. Dale, May 05 2011]

Examples

			59 = 30*1 + 29, the lower part of the twin prime pair 59,61.
		

Programs

Mathematica

30Range[0,60]+29 (* Harvey P. Dale, May 05 2011 *)

PARI

g(n) = forstep(x=29, n, 30, print1(x", "))