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Largest known twin primes and Sophie Germain primes
Author(s):
Karl-Heinz
Indlekofer;
Antal
Járai.
Journal:
Math. Comp.
68
(1999),
1317-1324.
MSC (1991):
Primary 11-04;
Secondary 11A41
Posted:
February 16, 1999
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Abstract:
The numbers are twin primes. The number is a Sophie Germain prime, i.e. and are both primes. For , the numbers , and are all primes.
References:
- 1.
- P. T. Bateman and R. A. Horn, A heuristic asymptotic formula concerning the distribution of prime numbers., Math. Comp. 16 (1962), 363-367. MR 26:6139
- 2.
- P. T. Bateman and R. A. Horn, Primes represented by irreducible polynomials in one variable., Theory of Numbers, Proc. Symp. Pure Math. Vol. VIII, Amer. Math. Soc., Providence, R. I., 1965, pp. 119-132. MR 31:1234
- 3.
- C. Caldwell, The largest known primes. A regularly updated list available on request, e-mail:caldwell@UTmartn.bitnet (1995).
- 4.
- H. Dubner, Large Sophie Germain Primes, Math. Comp. 65 (1996), 393-396. MR 96d:11008
- 5.
- K.-H. Indlekofer, A. Járai, Largest known twin primes, Math. Comp. 65 (1996), 427-428. MR 96d:11009
- 6.
- D. E. Knuth, The Art of Computer Programming, Vol. 1-3. Second Edition, Addison-Wesley, 1981. MR 83i:68003
- 7.
- P. Ribenboim, The Book of Prime Number Records, Springer-Verlag, 1989. MR 90g:11127
- 8.
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- 9.
- H. Riesel, Lucasian criteria for the primality of
, Math. Comp. 23 (1969), 869-875. MR 41:6773 - 10.
- B. K. Parady, J. F. Smith, S. E. Zarantonello, Largest known twin primes, Math. Comp. 55 (1990), 381-382. MR 90j:11013
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Additional Information:
Karl-Heinz
Indlekofer
Affiliation:
Universität GH Paderborn, FB 17, D-33095 Paderborn, Germany
Email:
k-heinz@uni-paderborn.de
Antal
Járai
Affiliation:
Universität GH Paderborn, FB 17, D-33095 Paderborn, Germany
Email:
jarai@uni-paderborn.de
DOI:
10.1090/S0025-5718-99-01079-0
PII:
S 0025-5718(99)01079-0
Received by editor(s):
April 7, 1997
Received by editor(s) in revised form:
February 5, 1998
Posted:
February 16, 1999
Copyright of article:
Copyright
1999,
American Mathematical Society
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