Primeness of Sevens

how the dice roll

The combination of possible rolls of the dice.

Since this month is devoted to the ins and outs of seven-ness, I thought a few facts would be appropriate.

So, here from Wikipedia, are some of the features of this prime number, which serve to prove that mathematics is a language of alien thought about real correspondences between imaginary concepts (All numbers, including seven, are imaginary. Try to find one.)

“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.”

“A safe prime is a prime number of the form 2p + 1, where p is also a prime. (Conversely, the prime p is a Sophie Germain prime.) This is considered important in cryptography: for instance, the ANSI X9.31 standard mandates that strong primes (not safe primes) be used for RSA moduli. I guess that strong primes are the dangerous ones.”

“In number theory, a lucky number is a natural number in a set which is generated by a ‘sieve’ similar to the Sieve of Eratosthenes that generates the primes.”

“A happy number is defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are happy numbers, while those that do not end in 1 are unhappy numbers (or sad numbers).”

“In number theory, a Woodall number (Wn) is any natural number of the form
Wn = n × 2n − 1 for some natural number n. The first few Woodall numbers are:
1, 7, 23, 63, 159… Why that is a good thing is known only to Woodall.”

At this point, I lost the ability to parse the sentences as English. They were written primarily in math concepts, and I don’t know the language.

The one kind of math I can easily understand is that there are more ways to roll a seven with two cube dice than any other number, which makes me wonder even more why it’s so lucky to roll one.

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