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| - Dubner's conjecture is an as yet (2018) unsolved conjecture by American mathematician Harvey Dubner. It states that every even number greater than 4208 is the sum of two t-primes, where a t-prime is a prime which has a twin. The conjecture is computer-verified for numbers up to . Even numbers that make an exception are: 2, 4, 94, 96, 98, 400, 402, 404, 514, 516, 518, 784, 786, 788, 904, 906, 908, 1114, 1116, 1118, 1144, 1146, 1148, 1264, 1266, 1268, 1354, 1356, 1358, 3244, 3246, 3248, 4204, 4206, 4208.(sequence in the OEIS) (en)
- La conjecture de Dubner est une conjecture énoncée par Harvey Dubner, mathématicien amateur américain spécialisé dans la recherche de grands nombres premiers, selon laquelle : Si l'on appelle p-jumeau un nombre premier ayant un jumeau, alors tout nombre pair supérieur à 4208 est la somme de deux p-jumeaux. Les nombres pairs qui font exception sont : 2, 4, 94, 96, 98, 400, 402, 404, 514, 516, 518, 784, 786, 788, 904, 906, 908, 1114, 1116, 1118, 1144, 1146, 1148, 1264, 1266, 1268, 1354, 1356, 1358, 3244, 3246, 3248, 4204, 4206, 4208. (fr)
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| has abstract
| - Dubner's conjecture is an as yet (2018) unsolved conjecture by American mathematician Harvey Dubner. It states that every even number greater than 4208 is the sum of two t-primes, where a t-prime is a prime which has a twin. The conjecture is computer-verified for numbers up to . Even numbers that make an exception are: 2, 4, 94, 96, 98, 400, 402, 404, 514, 516, 518, 784, 786, 788, 904, 906, 908, 1114, 1116, 1118, 1144, 1146, 1148, 1264, 1266, 1268, 1354, 1356, 1358, 3244, 3246, 3248, 4204, 4206, 4208.(sequence in the OEIS) The conjecture, if proved, will prove both the Goldbach's conjecture (because it has already been verified that all the even numbers 2n, such that 2 < 2n ≤ 4208, are the sum of two primes) and the twin prime conjecture (there exists an infinite number of t-primes, and thus an infinite number of twin prime pairs). Whilst already itself a generalization of both these conjectures, the original conjecture of Dubner may be generalized even further:
* For each natural number k > 0, every sufficiently large even number n(k) is the sum of two d(2k)-primes, where a d(2k)-prime is a prime p which has a prime q such that d(p,q) = |q − p| = 2k and p, q successive primes. The conjecture implies the Goldbach's conjecture (for all the even numbers greater than a large value ℓ(k)) for each k, and Polignac's conjecture if we consider all the cases k. The original Dubner's conjecture is the case for k = 1.
* The same idea, but p and q are not necessarily consecutive in the definition of a d(2k)-prime. Again, the Dubner's conjecture is a case for k = 1. It implies the Goldbach's conjecture and the (if we consider all the cases k) are concerned. (en)
- La conjecture de Dubner est une conjecture énoncée par Harvey Dubner, mathématicien amateur américain spécialisé dans la recherche de grands nombres premiers, selon laquelle : Si l'on appelle p-jumeau un nombre premier ayant un jumeau, alors tout nombre pair supérieur à 4208 est la somme de deux p-jumeaux. Les nombres pairs qui font exception sont : 2, 4, 94, 96, 98, 400, 402, 404, 514, 516, 518, 784, 786, 788, 904, 906, 908, 1114, 1116, 1118, 1144, 1146, 1148, 1264, 1266, 1268, 1354, 1356, 1358, 3244, 3246, 3248, 4204, 4206, 4208. Cette conjecture a été vérifiée par logiciel pour tous les nombres pairs jusqu'à . Si cette conjecture était démontrée, cela prouverait à la fois la conjecture de Goldbach (tout nombre pair est la somme de deux nombres premiers) et la conjecture des nombres premiers jumeaux (il existe une infinité de nombres premiers jumeaux). (fr)
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