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Semiprime
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==Properties== Semiprime numbers have no [[composite number]]s as factors other than themselves.<ref>{{cite book|page=53|url=https://archive.org/stream/advancedarithme00frengoog#page/n58/mode/2up|title=Advanced Arithmetic for Secondary Schools|first=John Homer|last=French|year=1889|publisher=Harper & Brothers|location=New York}}</ref> For example, the number 26 is semiprime and its only factors are 1, 2, 13, and 26, of which only 26 is composite. For a squarefree semiprime <math>n=pq</math> (with <math>p\ne q</math>) the value of [[Euler's totient function]] <math>\varphi(n)</math> (the number of positive integers less than or equal to <math>n</math> that are [[relatively prime]] to <math>n</math>) takes the simple form <math display=block>\varphi(n)=(p-1)(q-1)=n-(p+q)+1.</math> This calculation is an important part of the application of semiprimes in the [[RSA cryptosystem]].<ref name=moe>{{cite book|title=The Mathematics of Encryption: An Elementary Introduction|volume=29|series=Mathematical World|first1=Margaret|last1=Cozzens|first2=Steven J.|last2=Miller|publisher=American Mathematical Society|year=2013|isbn=9780821883211|page=237|url=https://books.google.com/books?id=GbKyAAAAQBAJ&pg=PA237}}</ref> For a square semiprime <math>n=p^2</math>, the formula is again simple:<ref name=moe/> <math display=block>\varphi(n)=p(p-1)=n-p.</math>
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