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Mathematics of Computation

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On the lcm of the differences of eight primes

Author: François Morain
Journal: Math. Comp. 52 (1989), 225-229
MSC: Primary 11A41; Secondary 11A07, 11Y05
Corrigendum: Math. Comp. 54 (1990), 911.
Corrigendum: Math. Comp. 54 (1990), 911.
MathSciNet review: 971409
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Abstract: Following C. A. Spiro, who has found eight primes for which

$\displaystyle \operatorname{lcm}{({p_j} - {p_i})_{1 \leq i < j \leq 8}} = 5040,$

we show that for every set of eight odd primes $ \{ {q_1}, \ldots ,{q_8}\} $, one has $ 5040\vert\operatorname{lcm}({q_j} - {q_i})$. Moreover, $ \operatorname{lcm}({q_j} - {q_i}) = 5040$ infinitely often, under the assumption of the 8-tuple conjecture.

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Article copyright: © Copyright 1989 American Mathematical Society