## Prime Tuples

Prime tuples are pairs, triples, quadruples ... from neighboring prime numbers. In a broader sense, pairs of the form (p,p+4) or (p,p+6) are also included. The program determines all in an interval [a, b]

- Prime twins:
- These are prime number pairs of the form (p|p+2), i.e. with the difference 2.
- Prime cousins:
- These are prime number pairs of the form (p|p+4), i.e. with the difference 4.
- Sexy primes:
- These are prime number pairs of the form (p|p+6), i.e. with the difference 6.
- Prime triplets:
- These are triplet primes of the form (p|p+2|p+6) or the form [p|p+4|p+6].

In the program, the two forms are distinguished by the brackets and counted separately.

The triplet (3|5|7) are the only triplets of the form (p|p+2|p+4), since for p>3 one of the three numbers is alwaysdivisible by 3 .

### Example 1

Prime twins between 1 and 200 (3|5) (5|7) (11|13) (17|19) (29|31) (41|43) (59|61) (71|73) (101|103) (107|109) (137|139) (149|151) (179|181) (191|193) (197|199) 15 pairs of prime twins

### Example 2

Prime triplets between 1 and 100 (3|5|7) (5|7|11) [7|11|13] (11|13|17) [13|17|19] (17|19|23) [37|41|43] (41|43|47) [67|71|73] 9 triplet prime triplets 4 of the form (p|p+2|p+6) and 4 of the form [p|p+4|p+6]

See also:

Prime factorization

Wikipedia: Prime number | Integer factorization