Blum integer information

In mathematics, a natural number n is a Blum integer if n = p × q is a semiprime for which p and q are distinct prime numbers congruent to 3 mod 4.^[1] That is, p and q must be of the form 4t + 3, for some integer t. Integers of this form are referred to as Blum primes.^[2] This means that the factors of a Blum integer are Gaussian primes with no imaginary part. The first few Blum integers are

21, 33, 57, 69, 77, 93, 129, 133, 141, 161, 177, 201, 209, 213, 217, 237, 249, 253, 301, 309, 321, 329, 341, 381, 393, 413, 417, 437, 453, 469, 473, 489, 497, ... (sequence A016105 in the OEIS)

The integers were named for computer scientist Manuel Blum.^[3]

^ Joe Hurd, Blum Integers (1997), retrieved 17 Jan, 2011 from http://www.gilith.com/research/talks/cambridge1997.pdf
^ Goldwasser, S. and Bellare, M. "Lecture Notes on Cryptography" Archived 2012-04-21 at the Wayback Machine. Summer course on cryptography, MIT, 1996-2001
^ Sloane, N. J. A. (ed.). "Sequence A016105 (Blum integers: numbers of the form p * q where p and q are distinct primes congruent to 3 (mod 4))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

[HurdBlum-1] Joe Hurd, Blum Integers (1997), retrieved 17 Jan, 2011 from http://www.gilith.com/research/talks/cambridge1997.pdf

[GoldBell-2] Goldwasser, S. and Bellare, M. "Lecture Notes on Cryptography" Archived 2012-04-21 at the Wayback Machine. Summer course on cryptography, MIT, 1996-2001

[3] Sloane, N. J. A. (ed.). "Sequence A016105 (Blum integers: numbers of the form p * q where p and q are distinct primes congruent to 3 (mod 4))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

Blum integer information

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Natural number