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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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 | References | Similar Articles | Additional Information

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] R. Breusch, "Zur Verallgemeinerung des Bertrandschen Postulates, dass zwischen x und 2x stets Primzahlen liegen," Math. Z., v. 34, 1932, pp. 505-526. MR 1545270
  • [2] A. Makowski, "Partitions into unequal primes," Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., v. 8, 1960, pp. 125-126. (Russian) MR 22 #7991. MR 0117209 (22:7991)
  • [3] K. Molsen, "Zur Verallgemeinerung des Bertrandschen Postulates," Deutsche Math., v. 6, 1941, pp. 248-256. MR 8, 197. MR 0017770 (8:197d)
  • [4] H. E. Richert, "Über Zerlegungen in paarweise verschiedene Zahlen," Nordisk Mat. Tidskr., v. 31, 1949, pp. 120-122, MR 11, 646. MR 0034807 (11:646a)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1974-0340206-6
PII: S 0025-5718(1974)0340206-6
Keywords: Primes, congruence classes modulo 12
Article copyright: © Copyright 1974 American Mathematical Society