At one time, at Apple, we did what is now called a Rainbow Table password attack. We pre-computed a lot of passwords and could just do a “lookup” on the table to find the decryption. 1,374 more words

## Tags » Primes

#### Some Twin Primes

With representing the sum of all primes smaller than , the number is a member of the twin prime . The numbers and are also twin primes: and respectively. 19 more words

#### Idempotent elements in Rings

For a commutative ring an idempotent is an element such that . The collection is an ideal of and in fact, moreover, is a ring in its own right with identity (why?). 202 more words

#### Return list of primes up to n using for loop

I have just picked up learing python and I am trying to create a simple function which accepts an integer and returns a list of all primes from 2 to that integer. 197 more words

#### Le Monde puzzle [#1048]

**A**n arithmetic Le Monde mathematical puzzle:

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A magical integer m is such that the remainder of the division of any prime number p by m is either a prime number or 1.

#### Large Prime Factors of a Quadratic Polynomial

At the International Congress of Mathematicians in 1912, Landau posed four problems about prime numbers that he described as *“unattackable at the present state of mathematics.”* 782 more words

#### Leprechauns Know What It Feels

*To be human, that is*

Neil L. has graced these pages many times before. Every eve of St. Patrick’s Day he has visited Dick. Sometimes Dick has been hard to… 1,679 more words