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Chinese hypothesis
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The so-called Chinese hypothesis is a conjecture concerning a condition for primality mistakenly attributed by Jeans[1] to Chinese mathematicians from the time of Confucius.
Conjecture:
- An integer is a prime number if and only if .
It is easy to see by Fermat's little theorem that prime numbers satisfy this condition.
It is not clear that this conjecture was ever widely believed, though its proof was posed (anonymously) as a question in 1818.[2] The following year Frédéric Sarrus published a refutation with the smallest counterexample, 341 = 11 × 31.[3] (See A001567 for more counterexamples; see also A206786.)
Sarrus numbers
A001567 Pseudoprimes, also called Sarrus numbers: pseudoprimes to base 2.
- {341, 561, 645, 1105, 1387, 1729, 1905, 2047, 2465, 2701, 2821, 3277, 4033, 4369, 4371, 4681, 5461, 6601, 7957, 8321, 8481, 8911, 10261, 10585, 11305, 12801, 13741, 13747, ...}
References
- George P. Loweke, The Lore of Prime Numbers. New York: Vantage Press (1982): 22.
- ↑ J. H. Jeans, The converse of Fermat's theorem, Messenger of Mathematics 27 (1898), p. 174.
- ↑ Questions proposées, Annales de Gergonne 9 (1818-1819), p. 320.
- ↑ M. Frédéric Sarrus, Questions résolues. Démonstration de la fausseté du théorème énoncé à la page 320 du IX.e volume de ce recueil, Annales de Gergonne 10 (1819-1820), pp. 184-187.
External links
- Weisstein, Eric W., Chinese Hypothesis, from MathWorld—A Wolfram Web Resource. [http://mathworld.wolfram.com/ChineseHypothesis.html]
