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Arithmetic progressions consisting only of primes. (English) Zbl 0426.10007


MSC:

11A41 Primes
11N13 Primes in congruence classes
11B25 Arithmetic progressions
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References:

[1] W. A. GOLUBEV, ”Faktorisation der Zahlen der Form \( {x^3} \pm 4{x^2} + 3x \pm 1\),” Anz. Oesterreich. Akad. Wiss. Math.-Naturwiss. Kl., 1969, pp. 184-191.
[2] W. A. GOLUBEV, ”Faktorisation der Zahlen der Form \( {x^3} \pm 57\),” Anz. Oesterreich. Akad. Wiss. Math.-Naturwiss. Kl., 1969, pp. 191-194. · Zbl 0194.35002
[3] W. A. GOLUBEV, ”Faktorisation der Zahlen der Formen \( {x^3} \pm 83\) und \( {x^3} \pm 92009\),” Anz. Oesterreich. Akad. Wiss. Math.-Naturwiss. Kl., 1969, pp. 297-301. · Zbl 0206.33404
[4] W. A. GOLUBEV, ”Faktorisation der Zahlen der Form \( {x^3} + 4{x^2} - 25x + 13\),” Anz. Oesterreich. Akad. Wiss. Math.-Naturwiss. Kl., 1970, pp. 106-112. · Zbl 0199.36401
[5] E. GROSSWALD, ”Arithmetic progressions of primes.” (To appear.) · Zbl 0478.10034
[6] G. H. Hardy and J. E. Littlewood, Some problems of ’Partitio numerorum’; III: On the expression of a number as a sum of primes, Acta Math. 44 (1923), no. 1, 1 – 70. · JFM 48.0143.04 · doi:10.1007/BF02403921
[7] R. F. Faĭziev, The number of integers, expressible in the form of a sum of two primes, and the number of \?-twin pairs, Dokl. Akad. Nauk Tadžik. SSR 12 (1969), no. 2, 12 – 16 (Russian, with Tajiki summary).
[8] E. KARST, ”Lists of ten or more primes in arithmetical progression,” Scripta Math., v. 28, 1970, pp. 313-317. · Zbl 0198.36901
[9] Edgar Karst and S. C. Root, Teilfolgen von Primzahlen in arithmetischer Progression, Anz. Österreich. Akad. Wiss. Math.-Naturwiss. Kl. 1 (1972), 19 – 20. S. C. Root and Edgar Karst, Mehr Teilfolgen von Primzahlen in arithmetischer Progression, Anz. Österreich. Akad. Wiss. Math.-Naturwiss. Kl. 8 (1972), 178 – 179. · Zbl 0249.10004
[10] Edgar Karst and S. C. Root, Teilfolgen von Primzahlen in arithmetischer Progression, Anz. Österreich. Akad. Wiss. Math.-Naturwiss. Kl. 1 (1972), 19 – 20. S. C. Root and Edgar Karst, Mehr Teilfolgen von Primzahlen in arithmetischer Progression, Anz. Österreich. Akad. Wiss. Math.-Naturwiss. Kl. 8 (1972), 178 – 179. · Zbl 0249.10004
[11] Sol Weintraub, Seventeen primes in arithmetic progression, Math. Comp. 31 (1977), no. 140, 1030. · Zbl 0373.10005
[12] Sol Weintraub, Primes in arithmetic progression, Nordisk Tidskr. Informationsbehandling (BIT) 17 (1977), no. 2, 239 – 243. · Zbl 0362.10001
[13] D. ZAGIER, Private communication.
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