# prime triple

A prime triple is three consecutive primes, such that the first and the last differ by six. For example:

(5, 7, 11), (7, 11, 13), (11, 13, 17), (13, 17, 19), (17, 19, 23), (37, 41, 43), (41, 43, 47), (67, 71, 73), (97, 101, 103), and (101, 103, 107).

It is conjectured that there are infinitely many such
primes. In fact the Hardy-Littlewood prime k-tuple conjecture
suggests that the number less than *x* of each of the forms

- (
*p*,*p*+2,*p*+6) and - (
*p*,*p*+4,*p*+6)

is approximately

The actual numbers less than 100,000,000 are 55,600 and 55,556 respectively. The Hardy-Littlewood estimate above is 55,490.

**See Also:** PrimeConstellation, TwinPrime, Quadruple

**Related pages** (outside of this work)

- Prime
*k*-tuplets (includes the largest known prime triples)

**References:**

- Riesel94
H. Riesel,Prime numbers and computer methods for factorization, Progress in Mathematics Vol, 126, Birkhäuser Boston, 1994. Boston, MA, ISBN 0-8176-3743-5.MR 95h:11142[An excellent reference for those who want to start to program some of these algorithms. Code is provided in Pascal. Previous edition was vol. 57, 1985.]

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