Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

What is the biggest positive integer within 100 that can be/can not be written as the differences between two positive primes?

Can someone answer the cannot part?

There are two parts in the question.

Thanks in advance!

share|cite|improve this question
up vote 5 down vote accepted

Differences of primes are generally even (except when $2$ is involved).

$99$ can be written as $101 - 2$. Therefore a lower bound for the largest number which cannot be written as a difference of primes is $97$. It remains to check that $100$ and $98$ actually can be written as a difference of primes. Some simple trial and error will reveal that $$101 - 3 = 98$$ $$103 - 3 = 100$$

share|cite|improve this answer
What about the can not be part? – Victor Oct 16 '12 at 21:38
That's where $97$ comes in. – EuYu Oct 16 '12 at 21:44
Eu Yu - Thanks you very much. – Victor Oct 16 '12 at 21:45

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.