semiprime

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semiprime

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From semi- +‎ prime.

semiprime (plural semiprimes)

1. (number theory) A natural number that is the product of two (not necessarily distinct) prime numbers.
   • 2010, Jason Earls, The Lowbrow Experimental Mathematician, Lulu.com, page 145:

     Again, to be perfectly clear, we are looking for c values that produce a low density of semiprimes when employing Euler's basic polynomial but changing the c values, in the range of x=1 to 10000. Some very early standouts are: c=4 which produces 799 semiprimes; c=6 which produces 532 semiprimes; c=12 which produces only 431 semiprimes; c=18 which produces 364 semiprimes, and c=30 which produces only 320 semiprimes.

   • 2015, Jie Wang, Zachary A. Kissel, Introduction to Network Security: Theory and Practice, Wiley , page 113,

     Firstly, we should change semiprimes from time to time, where a particular semiprime should only be used in a time interval shorter than the time required to factor an RSA challenge number of a similar length. Secondly, we should use semiprimes that consist of more than 200 decimal digits.

   • 2015, Marius Coman, Two Hundred and Thirteen Conjectures on Primes: Collected Papers, Education Publishing, page 46:

     In this paper I will define four sequences of numbers obtained through concatenation, definitions which also use the notion of “sum of the digits of a number”, sequences that have the property to produce many primes, semiprimes and products of very few prime factors.

• (product of two primes, not necessarily distinct): biprime

• discrete semiprime
• distinct semiprime

semiprime (not comparable)

1. (mathematics) That has properties derived directly or by extension from a semiprime.
   • 1974, Thomas W. Hungerford, Algebra, Springer, page 446:

     The final part of the semiprime-semisimple analogy is given by
     Proposition 4.4. A ring ${\displaystyle \mathbf {R} }$ is semiprime if and only if ${\displaystyle \mathbf {R} }$ is isomorphic to a subdirect product of prime rings.

   • 1982, K. A. Zhevlakov, A. M. Slin'ko, I. P. Shestakov, A. I. Shirshov, translated by Harry F. Smith, Rings That Are Nearly Associative, Academic Press, page 176:

     In this chapter we shall study the structure of semiprime alternative algebras.

   • 2003, John N. Mordeson, Davender S. Malik, Nobuaki Kuroki, Fuzzy Semigroups, Springer, page 213:

     Let ${\displaystyle f}$ be a semiprime fuzzy ideal of ${\displaystyle S}$ and ${\displaystyle x\in S}$.

• Semiprime ideal on Wikipedia.Wikipedia
• Semiprime ring on Wikipedia.Wikipedia
• Semiprime on Wolfram MathWorld