Mathematics, Number theory, Sciences A natural number that is the product of two (not necessarily distinct) prime numbers.
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.2010, Jason Earls, The Lowbrow Experimental Mathematician, Lulu.com, page 145:
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.
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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.2015, Marius Coman, Two Hundred and Thirteen Conjectures on Primes: Collected Papers, Education Publishing, page 46:
Mathematics, Sciences That has properties derived directly or by extension from a semiprime.
The final part of the semiprime-semisimple analogy is given by Proposition 4.4. A ring #92;mathbf#123;R#125; is semiprime if and only if #92;mathbf#123;R#125; is isomorphic to a subdirect product of prime rings.1974, Thomas W. Hungerford, Algebra, Springer, page 446:
In this chapter we shall study the structure of semiprime alternative algebras.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:
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Let f be a semiprime fuzzy ideal of S and x#92;inS.2003, John N. Mordeson, Davender S. Malik, Nobuaki Kuroki, Fuzzy Semigroups, Springer, page 213: