Seven, the fourth prime number, is not only a Mersenne prime (since 23 − 1 = 7) but also a double Mersenne prime since the exponent, 3, is itself a Mersenne prime. It is also a Newman–Shanks–Williams prime, a Woodall prime, a factorial prime, a lucky prime, a happy number (happy prime), a safe prime (the only Mersenne safe prime), and the fourth Heegner number.
Seven is the lowest natural number that cannot be represented as the sum of the squares of three integers. (See Lagrange's four-square theorem#Historical development.)
7 is the only number D for which the equation 2n − D = x2 has more than two solutions for n and x natural. In particular, the equation 2n − 7 = x2 is known as the Ramanujan–Nagell equation.
999,999 divided by 7 is exactly 142,857. Therefore, when a vulgar fraction with 7 in the denominator is converted to a decimal expansion, the result has the same six-digit repeating sequence after the decimal point, but the sequence can start with any of those six digits. For example, 1/7 = 0.142857 142857... and 2/7 = 0.285714 285714....
In fact, if one sorts the digits in the number 142,857 in ascending order, 124578, it is possible to know from which of the digits the decimal part of the number is going to begin with. The remainder of dividing any number by 7 will give the position in the sequence 124578 that the decimal part of the resulting number will start. For example, 628 ÷ 7 = 89 5/7; here 5 is the remainder, and would correspond to number 7 in the ranking of the ascending sequence. So in this case, 628 ÷ 7 = 89.714285. Another example, 5238 ÷ 7 = 748 2/7, hence the remainder is 2, and this corresponds to number 2 in the sequence. In this case, 5238 ÷ 7 = 748.285714.
But you knew all that. Here’s some random crap from my Big Book O’Seven.
A seven-sided shape is a heptagon. The regular n-gons for n ≤ 6 can be constructed by compass and straightedge alone, but the regular heptagon cannot. Figurate numbers representing heptagons (including seven) are called heptagonal numbers. Seven is also a centered hexagonal number.
There are seven fundamental types of catastrophes. It’s true. Look it up. One is called “Only chair left is next to Danny”.
Something oddly aligned about 700 games and a 7 nil scoreline. A sizzling penalty save. A slashing drive from Banshee, a girly dink from Satan, a bosom bump from a bewildered Raggster, a pornographic ankles around the neck face ferret from Chacal, a shin here, a knee there, a trapezoid there. Seven goals for seven (plus 11) brothers.
Seven colours of the rainbow, seven bridges of Corinth, seven days in the week, Seven Sages of the Bamboo Grove, seven wonders of the ancient world, seven hills of Rome, 7 No 1 hits on Band on the Run, 7 inches of terror down Marky Mark’s velvet sweat pants, 7 the size of Mingus boots, 7 considered a God number in ancient Egypt. The Pharaoh usually ordered things in groups of multiples of 7. For a time, 7 was not even used in writings for the people of Egypt.
7 pure notes in the diatonic scale.
Gyles says it’s tight at the top. Satan says it’s even tighter at the bottom, although he may have got the wrong end the brownstick.
So far the season has been a disaster, on that we can all agree. The farce moves to Kura St next week, god help us. Don’t bring the kids.
I leave you with this (again):
7 is the lowest dimension of a known exotic sphere, although there may exist as yet unknown exotic smooth structures on the 4-dimensional sphere. I nominate Doc as our very own exotic sphere. He is quite smooth, but we can all agree that 3 dimensions is enough.