Largest known twin primes

and Sophie Germain primes

Authors:
Karl-Heinz Indlekofer and Antal Járai

Journal:
Math. Comp. **68** (1999), 1317-1324

MSC (1991):
Primary 11-04; Secondary :, 11A41

DOI:
https://doi.org/10.1090/S0025-5718-99-01079-0

Published electronically:
February 16, 1999

MathSciNet review:
1642750

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

**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.**P. Ribenboim,*The New Book of Prime Number Records*, Springer-Verlag, 1996. MR**96k:11112****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:
https://doi.org/10.1090/S0025-5718-99-01079-0

Received by editor(s):
April 7, 1997

Received by editor(s) in revised form:
February 5, 1998

Published electronically:
February 16, 1999

Article copyright:
© Copyright 1999
American Mathematical Society