Day 280

October 9, 2017

Pat Ballew is a retired math teacher who writes a blog On This Day In Math that gives a day-by-day history of mathematics. The blog is odd, quirky, and unquestionably fun. On October 7th, Ballew wrote:

The 280th day of the year…. The sum of the first 280 consecutive primes, mod 280, is prime.

Since I like to play with prime numbers, that got my attention, and I quickly went to determine how many such days there are in a year.

Your task is to determine how many days in a year share the characteristic that on the nth day the sum of the first n primes, mod n, is prime. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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