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In number theory, Bonse's inequality, named after H. Bonse,[1] relates the size of a primorial to the smallest prime that does not appear in its prime factorization. It states that ifp1, ..., pnpn+1 are the smallest n + 1 prime numbers and n ≥ 4, then

\( p_1 \cdots p_n > p_{n+1}^2. \, \)


Bonse, H. (1907). "Über eine bekannte Eigenschaft der Zahl 30 und ihre Verallgemeinerung". Archiv der Mathematik und Physik 3 (12): 292–295.


Uspensky, J. V.; Heaslet, M. A. (1939). Elementary Number Theory. New York: McGraw Hill. p. 87.
Zhang, Shaohua (2009). "A new inequality involving primes". v1. arXiv:0908.2943

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