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Sums of distinct primes from congruence classes modulo $ 12$


Authors: Robert E. Dressler, Andrzej Makowski and Thomas Parker
Journal: Math. Comp. 28 (1974), 651-652
MSC: Primary 10J15
MathSciNet review: 0340206
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Abstract: It is shown that every integer greater than 1969, 1349, 1387, 1475 is a sum of distinct primes of the form $ 12k + 1,12k + 5,12k + 7,12k + 11$, respectively. Furthermore, these lower bounds are best possible.


References [Enhancements On Off] (What's this?)

  • [1] Robert Breusch, Zur Verallgemeinerung des Bertrandschen Postulates, daß zwischen 𝑥 und 2 𝑥 stets Primzahlen liegen, Math. Z. 34 (1932), no. 1, 505–526 (German). MR 1545270, 10.1007/BF01180606
  • [2] A. Mąkowski, Partitions into unequal primes, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 8 (1960), 125–126 (English, with Russian summary). MR 0117209
  • [3] Karl Molsen, Zur Verallgemeinerung des Bertrandschen Postulates, Deutsche Math. 6 (1941), 248–256 (German). MR 0017770
  • [4] Hans-Egon Richert, Über Zerlegungen in paarweise verschiedene Zahlen, Norsk Mat. Tidsskr. 31 (1949), 120–122 (German). MR 0034807

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1974-0340206-6
Keywords: Primes, congruence classes modulo 12
Article copyright: © Copyright 1974 American Mathematical Society