Bonse's inequality

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 if p₁, ..., p_n, p_n+1 are the smallest n + 1 prime numbers and n ≥ 4, then

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

Notes

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

References

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