Long arithmetic progressions of primes: some old, some new

Author:
Paul A. Pritchard

Journal:
Math. Comp. **45** (1985), 263-267

MSC:
Primary 11B25; Secondary 11Y55

DOI:
https://doi.org/10.1090/S0025-5718-1985-0790659-1

MathSciNet review:
790659

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Abstract: The results are reported of an extensive search with a computer for "long" arithmetic progressions of primes. Such progressions with minimum last term are now known for all lengths up to and including nineteen.

**[1]**S. Chowla, "There exist an infinity of 3-combinations of primes in A. P.,"*Proc. Lahore Philos. Soc.*, v. 6, 1944, pp. 15-16. MR**0014125 (7:243l)****[2]**E. Grosswald, "Arithmetic progressions that consist only of primes,"*J. Number Theory*, v. 14, 1982, pp. 9-31. MR**644898 (83k:10081)****[3]**E. Grosswald & P. Hagis, Jr., "Arithmetic progressions consisting only of primes,"*Math. Comp.*, v. 33, 1979, pp. 1343-1352. MR**537981 (80k:10054)****[4]**R. K. Guy,*Unsolved Problems in Number Theory*, Springer-Verlag, New York, 1981. MR**656313 (83k:10002)****[5]**G. H. Hardy & J. E. Littlewood, "Some problems of 'partitio numerorum' III: on the expression of a number as a sum of primes,"*Acta Math.*, v. 44, 1923, pp. 1-70. MR**1555183****[6]**D. R. Heath-Brown, "Three primes and an almost prime in arithmetic progression,"*J. London Math. Soc.*(2), v. 23, 1981, pp. 396-414. MR**616545 (82j:10074)****[7]**E. Karst, "12-16 primes in arithmetical progression,"*J. Recreational Math.*, v. 2, 1969, pp. 214-215. MR**0252345 (40:5566)****[8]**E. Karst, "Lists of ten or more primes in arithmetical progressions,"*Scripta Math.*, v. 28, 1970, pp. 313-317.**[9]**E. Karst & S. C. Root, "Teilfolgen von Primzahlen in arithmetischer Progression,"*Anz. Österreich. Akad. Wiss. Math.-Natur. Kl.*, 1972, pp. 19-20 (see also pp. 178-179). MR**0409326 (53:13086a)****[10]**P. A. Pritchard, "A case study of number-theoretic computation: searching for primes in arithmetic progression,"*Sci. Comput. Programming*, v. 3, 1983, pp. 37-63. MR**730934 (85g:11119)****[11]**P. A. Pritchard, "Eighteen primes in arithmetic progression,"*Math. Comp.*, v. 41, 1983, p. 697. MR**717714 (85c:11125)****[12]**S. Weintraub, "Primes in arithmetic progression,"*BIT*, v. 17, 1977, pp. 239-243. MR**0491446 (58:10695)****[13]**S. Weintraub, "Seventeen primes in arithmetic progression,"*Math. Comp.*, v. 31, 1977, p. 1030. MR**0441849 (56:240)**

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DOI:
https://doi.org/10.1090/S0025-5718-1985-0790659-1

Article copyright:
© Copyright 1985
American Mathematical Society