Prime Triplet
المؤلف:
Hardy, G. H. and Wright, E. M
المصدر:
An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, 1979.
الجزء والصفحة:
...
9-9-2020
1327
Prime Triplet
A prime triplet is a prime constellation of the form (
, 
, 
), (
, 
, 
), etc. Hardy and Wright (1979, p. 5) conjecture, and it seems almost certain to be true, that there are infinitely many prime triplets of the form (
, 
, 
) and (
, 
, 
).
| triplet |
Sloane |
first member |
( ,  ,  ) |
A022004 |
5, 11, 17, 41, 101, 107, ... |
( ,  ,  ) |
A046134 |
3, 5, 11, 29, 59, 71, 101, ... |
( ,  ,  ) |
A046135 |
5, 11, 17, 29, 41, 59, 71, ... |
( ,  ,  ) |
A022005 |
7, 13, 37, 67, 97, 103, ... |
( ,  ,  ) |
A046136 |
3, 7, 13, 19, 37, 43, 79, ... |
( ,  ,  ) |
A046137 |
7, 19, 67, 97, 127, 229, ... |
( ,  ,  ) |
A046138 |
5, 11, 23, 53, 101, 131, ... |
( ,  ,  ) |
A046139 |
7, 13, 31, 37, 61, 73, 97, ... |
( ,  ,  ) |
A023241 |
5, 7, 11, 17, 31, 41, 47, ... |
( ,  ,  ) |
A046141 |
5, 11, 29, 59, 71, 89, 101, ... |
As of Apr. 2019, the largest known prime triplet of the form 
has smallest member
and each of its three members has 
decimal digits.
REFERENCES:
Forbes, T. "Prime 
-Tuplets." https://anthony.d.forbes.googlepages.com/ktuplets.htm.
Hardy, G. H. and Wright, E. M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, 1979.
Rivera, C. "Problems & Puzzles: Puzzle 034-Prime Triplets in Arithmetic Progression." https://www.primepuzzles.net/puzzles/puzz_034.htm.
Sloane, N. J. A. Sequences A022004, A022005, A023241, A046134, A046135, A046136, A046137, A046138, A046139, and A046141in "The On-Line Encyclopedia of Integer Sequences."
الاكثر قراءة في نظرية الاعداد
اخر الاخبار
اخبار العتبة العباسية المقدسة
