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Kapitel 5
1948 Gunderson, N.G.Derivation of Criteria for the First Case of Fermat’s Last Theorem and the Combination of these Criteria to Produce a New Lower Bound for the Exponent. Dissertation, Cornell University, 1948, 111 Seiten.
1951 Dénes, P. An extension of Legendre’s criterion in connection with the first case of Fermat’s last theorem. Publ. Math. Debrecen 2 (1951), 115–120.
1953 Goldberg, K. A table of Wilson quotients and the third Wilson prime. J. London Math. Soc. 28 (1953), 252–256.
1954 Ward, M. Prime divisors of second order recurring sequences. Duke Math. J. 21 (1954), 607–614.
1956 Obláth, R. Une propriété des puissances parfaites. Mathesis 65 (1956), 356–364.
1956 Riesel, H. Några stora primtal. Elementa 39 (1956), 258–260.
1958 Jarden, D.Recurring Sequences. Riveon Lematematika, Jerusalem 1958 (3. Auflage bei Fibonacci Assoc., San Jose, CA 1973).
1958 Robinson, R.M. A report on primes of the form k · 2n +1 and on factors of Fermat numbers. Proc. Amer. Math. Soc. 9 (1958), 673–681.
1960 Sierpiński, W. Sur un problème concernant les nombres k · 2n + 1. Elem. Math. 15 (1960), 73–74.
1964 Graham, R.L. A Fibonacci-like sequence of composite numbers. Math. Mag. 37 (1964), 322–324.
1964 Riesel, H. Note on the congruence ap−1≡ 1 (mod p2). Math. Comp. 18 (1964), 149–150.
1964 Siegel, C.L. Zu zwei Bemerkungen Kummers. Nachr. Akad. d. Wiss. Göttingen, Math. Phys. Kl., II, 1964, 51–62. Nachdruck in Gesammelte Abhandlungen (Hrsg. K. Chandrasekharan und H. Maas), Bd. III, 436–442. Springer-Verlag, Berlin 1966.
1965 Kloss, K.E. Some number theoretic calculations. J. Res. Nat. Bureau of Stand. B, 69 (1965), 335–336.
1966 Hasse, H. Über die Dichte der Primzahlen p, für die eine vorgegebene ganzrationale Zahl a ≠ 0 von gerader bzw. ungerader Ordnung mod p ist. Math. Ann. 168 (1966), 19–23.
1966 Kruyswijk, D.On the congruence up−1 ≡ 1 (mod p2) (niederländisch). Math. Centrum Amsterdam, 1966, 7 Seiten.
1969 Riesel, H. Lucasian criteria for the primality of N = h · 2n−1. Math. Comp. 23 (1969), 869–875.
1971 Brillhart, J., Tonascia, J. & Weinberger, P.J. On the Fermat quotient. In Computers in Number Theory (Hrsg. A.L. Atkin und B.J. Birch), 213–222. Academic Press, New York 1971.
1975 Johnson, W. Irregular primes and cyclotomic invariants. Math. Comp. 29 (1975), 113–120.
1976 Hooley, C.Application of Sieve Methods to the Theory of Numbers. Cambridge Univ. Press, Cambridge 1976.
1978 Wagstaff Jr., S.S. The irregular primes to 125000. Math. Comp. 32 (1978), 583–591.
1978 Williams, H.C. Some primes with interesting digit patterns. Math. Comp. 32 (1978), 1306–1310.
1979 Erdös, P. & Odlyzko, A.M. On the density of odd integers of the form (p − 1)2−n and related questions. J. Number Theory 11 (1979), 257–263.
1979 Ribenboim, P.13 Lectures on Fermat’s Last Theorem. Springer-Verlag, New York 1979.
1979 Williams, H.C. & Seah, E. Some primes of the form (an − 1)/(a − 1). Math. Comp. 33 (1979), 1337–1342.
1980 Newman, M., Shanks, D. & Williams, H.C. Simple groups of square order and an interesting sequence of primes. Acta Arith. 38 (1980), 129–140.
1980 Powell, B. Primitive densities of certain sets of primes. J. Number Theory 12 (1980), 210–217.
1981 Lehmer, D.H. On Fermat’s quotient, base two. Math. Comp. 36 (1981), 289–290.
1982 Powell, B. Problem E 2956 (The existence of small prime solutions of xp−1 ≢ 1 (mod p2)). Amer. Math. Monthly 89 (1982), S. 498.
1982 Yates, S.Repunits and Repetends. Star Publ. Co., Boynton Beach, FL 1982.
1983 Jaeschke, G. On the smallest k such that k · 2N + 1 are composite. Math. Comp. 40 (1983), 381–384; Corrigendum, 45 (1985), S. 637.
1983 Keller, W. Factors of Fermat numbers and large primes of the form k · 2n +1. Math. Comp. 41 (1983), 661–673.
1983 Ribenboim, P. 1093. Math. Intelligencer 5, No. 2 (1983), 28–34.
1985 Lagarias, J.C. The set of primes dividing the Lucas numbers has density 2/3. Pacific J. Math. 118 (1985), 19–23.
1986 Tzanakis, N. Solution to problem E2956. Amer. Math. Monthly 93 (1986), S. 569.
1986 Williams, H.C. & Dubner, H. The primality of R1031. Math. Comp. 47 (1986), 703–711.
1987 Granville, A.Diophantine Equations with Variable Exponents with Special Reference to Fermat’s Last Theorem. Dissertation, Queen’s University, Kingston, Ontario 1987, 207 Seiten.
1987 Rotkiewicz, A. Note on the diophantine equation 1+x+x2+ · · · + xn = ym. Elem. Math. 42 (1987), s. 76
1988 Brillhart, J., Montgomery, P.L. & Silverman, R.D. Tables of Fibonacci and Lucas factorizations, and Supplement. Math. Comp. 50 (1988), 251–260 und S1–S15.
1988 Gonter, R.H. & Kundert, E.G.Wilson’s theorem (n − 1)! ≡ − 1 (mod p2) has been computed up to 10,000,000. Fourth SIAM Conference on Discrete Mathematics, San Francisco 1988.
1988 Granville, A. & Monagan, M.B. The first case of Fermat’s last theorem is true for all prime exponents up to 714,591,416,091, 389. Trans. Amer. Math. Soc. 306 (1988), 329–359.
1989 Dubner, H. Generalized Cullen numbers. J. Recr. Math. 21 (1989), 190–194.
1989 Löh, G. Long chains of nearly doubled primes. Math. Comp. 53 (1989), 751–759.
1989 Tanner, J.W. & Wagstaff, Jr., S.S. New bound for the first case of Fermat’s last theorem. Math. Comp. 53 (1989), 743–750.
1990 Brown, J., Noll, L.C., Parady, B.K., Smith, J.F., Smith, G. W. & Zarantonello, S. Letter to the editor. Amer. Math. Monthly 97 (1990), S. 214.
1990 Knuth, D.E. A Fibonacci-like sequence of composite numbers. Math. Mag. 63 (1990), 21–25.
1991 Aaltonen, M. & Inkeri, K. Catalan’s equation xp−yq = 1 and related congruences. Math. Comp. 56 (1991), 359–370. Nachdruck in Collected Papers of Kustaa Inkeri (Hrsg. T. Metsänkylä und P. Ribenboim), Queen’s Papers in Pure and Appl. Math. 91. Queen’s Univ., Kingston, Ontario 1992.
1991 Fee, G. & Granville, A. The prime factors of Wendt’s binomial circulant determinant. Math. Comp. 57 (1991), 839–848.
1991 Keller, W. Woher kommen die größten derzeit bekannten Primzahlen? Mitt. Math. Ges. Hamburg 12 (1991), 211–229.
1992 Buhler, J.P., Crandall, R.E. & Sompolski, R.W. Irregular primes to one million. Math. Comp. 59 (1992), 717–722.
1993 Buhler, J.P., Crandall, R.E., Ernvall, R. & Metsänkylä T., Irregular primes and cyclotomic invariants to four million. Math. Comp. 61 (1993), 151–153.
1993 Dubner, H. Generalized repunit primes. Math. Comp. 61 (1993), 927–930.
1993 Montgomery, P.L. New solutions of ap−1≢ 1 (mod p2). Math. Comp. 61 (1993), 361–363.
1994 Crandall, R.E. & Fagin, B. Discrete weighted transforms and large-integer arithmetic. Math. Comp. 62 (1994), 305–324.
1994 Gonter, R.H. & Kundert, E.G.All prime numbers up to 18,876,041 have been tested without finding a new Wilson prime. Unveröffentlichtes Manuskript, Amherst, MA 1994, 10 Seiten.
1994 Suzuki, J. On the generalized Wieferich criteria. Proc. Japan Acad. Sci. A (Math. Sci.), 70 (1994), 230–234.
1995 Keller, W. New Cullen primes. Math. Comp. 64 (1995), 1733–1741.
1995 Keller, W. & Niebuhr, W. Supplement to “New Cullen primes”. Math. Comp. 64 (1995), S39–S46.
1997 Crandall, R., Dilcher, K. & Pomerance, C. A search for Wieferich and Wilson primes. Math. Comp. 66 (1997), 433–449.
1997 Ernvall, R. & Metsänkylä, T. On the p-divisibility of Fermat quotients. Math. Comp. 66 (1997), 1353–1365.
1999 Dubner, H. & Keller, W. New Fibonacci and Lucas primes. Math. Comp. 68 (1999), 417–427 and S1–S12.
1999 Forbes, T. Prime clusters and Cunninghamchains. Math. Comp. 68 (1999), 1739–1747.
1999 Ribenboim, P.Fermat’s Last Theorem for Amateurs. Springer-Verlag, New York 1999.
2000 Pinch, R.G.E. The pseudoprimes up to 1013. In Proc. Fourth Int. Symp. on Algorithmic Number Th. (Hrsg. W. Bosma). Lecture Notes in Computer Sci. #1838, 459–474. Springer-Verlag, New York 2000.
2001 Buhler, J., Crandall, R., Ernvall, R., Metsänkylä, T. & Shokrollahi, M.A. Irregular primes and cyclotomic invariants to 12 million. J. Symbolic Comp. 31 (2001), 89–96.
2002 Dubner, H. Repunit R49081 is a probable prime. Math. Comp. 71 (2002), 833–835.
2002 Dubner, H. & Gallot, Y. Distribution of generalized Fermat prime numbers. Math. Comp. 71 (2002), 825–832.
2002 Izotov, A.S. Second-order linear recurrences of composite numbers. Fibonacci Quart. 40 (2002), 266–268.
2002 Sellers, J.A. & Williams, H.C. On the infinitude of composite NSW numbers. Fibonacci Quart. 40 (2002), 253–254.
2005 Keller, W. & Richstein, J. Solutions of the congruence ap−1 ≡ 1 (mod pr). Math. Comp. 74 (2005), 927–936.
2005 Knauer, J. & Richstein, J. The continuing search for Wieferich primes. Math. Comp. 74 (2005), 1559–1563.
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(2006). Welche besonderen Arten von Primzahlen wurden untersucht?. In: Die Welt der Primzahlen. Springer-Lehrbuch. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-34284-2_6
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