# prime

## Bit flipping to primes

Someone asked an interesting question on MathOverflow: given an odd number, can you always flip a bit in its binary…

## How probable is a probable prime?

A probable prime is a number that passes a test that all primes pass and that most composite numbers fail.…

## Relatively prime determinants

Suppose you fill two n×n matrices with random integers. What is the probability that the determinants of the two matrices…

## Prime plus power of 2

A new article [1] looks at the problem of determining the proportion of odd numbers that can be written as…

## Estimating the proportion of smooth numbers

A number is said to be “smooth” if all its prime factors are small. To make this precise, a number…

## Prime numbers and Goldbach’s conjecture visualization.

isn’t it?The German mathematician G. F. B. Riemann (1826–1866) observed that the distribution of prime numbers is very closely related…

## Share The π: Honoring Neglected Mathematical Constants

Subsequent occurrences are fairly common. Brun’s and Meissel-Mertens ConstantsPrime numbers make an appearance in two fascinating constants we’ll discuss next.…

## Python Pro Tip: Use Itertools, Generators, and Generator Expressions

Think of the memory such a list would occupy. It would be great if we had something that could just…

## Strong primes

There are a couple different definitions of a strong prime. In number theory, a strong prime is one that is…

## Goldilocks and the three multiplications

Mike Hamburg designed an elliptic curve for use in cryptography he calls Ed448-Goldilocks. The prefix Ed refers to the fact…

## Tricks for arithmetic modulo NIST primes

The US National Institute of Standards and Technology (NIST) originally recommended 15 elliptic curves for use in elliptic curve cryptography…

## Elliptic curve P-384

Possibly, but they have reasons to recommend methods that they believe foreign governments cannot break. The equation of the P-384…

## New prime record: 51st Mersenne prime discovered

The largest known prime is nowWritten in hexadecimal the newly discovered prime isFor decades the largest known prime has been…

## Code doodling: isPrime

Then I’ll run the code on my laptop and time the results for each algorithm testing for primes in the…

## Prime numbers in complex domains are actually quite simple

Likewise, a number in Z[√−2] is said to be divisible by another number in Z[√−2] if the result of the…