The second Mersenne prime M_3=2^3-1, which is itself the exponent of Mersenne prime M_7=2^7-1=127. It gives rise to the perfect number P_7=M_7·2^6=8128. It is a Gaussian prime, but not an Eisenstein prime, since it factors as 7=(2-omega)(2-omega^2), where omega is a primitive cube root of unity. It is the smallest non-Sophie Germain prime. It is also the smallest non-Fermat prime, and as such is the smallest number of faces of a regular polygon (the heptagon) that is not constructible by straightedge and compass.

It occurs as a sacred number in the Bible and in various other traditions. In Babylonian numerology it was considered as the perfect number, the only number between 2 and 10 which is not generated (divisible) by any other number, nor does it generate (divide) any other number.

Words referring to number seven may have the prefix hepta-, derived from the Greek epsilon^'pitaualpha-) (heptic), or sept- (septuple), derived from the Latin septem.

See also

Casting Out Sevens, Heptagon, Heptahedron, One-Seventh Ellipse, Seven Circles Theorem

This entry contributed by Margherita Barile

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Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, pp. 70-71, 1986.

Cite this as:

Barile, Margherita. "7." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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