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# Category Archives: primes

## Triangunit divisors and quadratic reciprocity

Recall that the triangunit numbers are defined as the numbers you get by appending the digit 1 to the end of triangular numbers. Put another way, where denotes the th triangular number, and the th triangunit number. The challenge, posed … Continue reading

Posted in arithmetic, modular arithmetic, number theory, primes, proof
Tagged OEIS, quadratic, reciprocity, triangular, triangunit
5 Comments

## Prime Time in Haskell

In a recent blog post, Patrick Vennebush of Math Jokes 4 Mathy Folks noted that 2011 can be expressed as a sum of consecutive prime numbers, and challenged his readers to work out how. He also posed a couple further … Continue reading

Posted in arithmetic, number theory, primes, programming
Tagged consecutive, Haskell, primes, sum
8 Comments

## Book Review: The Mystery of the Prime Numbers

Several months ago, Matthew Watkins sent me a review copy of his new book, Secrets of Creation Volume One: The Mystery of the Prime Numbers. It’s taken me a while to get around to reviewing it, but not for lack … Continue reading

Posted in books, number theory, primes, review
Tagged book review, mystery, numbers, prime
3 Comments

## MMM #33: Super divisible

This week’s Monday Math Madness is up at Wild About Math!. Looks like a fairly accessible problem this week: What’s the prime factorization of the smallest whole number that is divisible by all integers from 1 up to and including … Continue reading

Posted in challenges, links, number theory, primes
Tagged divisible, factorization, smallest

## More on repetend lengths

In a previous post, I noted that the length of the repetend (repeating portion of the decimal expansion) of a fraction with prime denominator p is at most p-1, and in fact divides p-1. I also said: In fact, there’s … Continue reading

Posted in group theory, number theory, pattern, primes
Tagged decimal, expansion, fractions, length, repetend
6 Comments

## Two Very Large primes

As promised, I can now reveal the identity of the two newly discovered Mersenne primes. The smaller of the two, discovered on September 6 by Hans-Michael Elvenich in Langenfeld, Germany, is an 11,185,272-digit number which you can download here. The … Continue reading

## New Mersenne primes!

The Great Internet Mersenne Prime Search just announced not one, but two new Mersenne primes! You might also recall the last time they announced a new prime, in September 2006, so these new primes were found almost exactly two years … Continue reading

Posted in computation, famous numbers, links, primes
Tagged announcement, discovery, GIMPS, Mersenne, prime
1 Comment

## Perfect numbers, part III

This is the last in a series of posts about perfect numbers. A quick recap of the series so far: in part I, I defined perfect numbers as positive integers n for which , where denotes the sum of the … Continue reading

Posted in algebra, number theory, open problems, primes, solutions
11 Comments

## Prime Shooter!

Today I came across this nifty Space Invaders-like game — except instead of shooting bullets at UFOs, you shoot prime factors at integers. For example, if the number 66 is falling towards you, you need to shoot it with 2, … Continue reading

Posted in games, primes
2 Comments

## Open problems: Twin prime conjecture

Oops, so much for posting once a week! My excuse is that I’ve been hard at work on my book. Well, nothing to do but get right back at it. I promise* I will be better** about posting regularly*** from … Continue reading

Posted in challenges, famous numbers, infinity, primes
3 Comments