semiprime

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 [under licence from Higher Education Press], 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, Harry F. Smith (translator), K. A. Zhevlakov, A. M. Slin'ko, I. P. Shestakov, A. I. Shirshov, 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