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 smallest positive common difference of a 6-term arithmetic progression consisting entirely of (positive) prime numbers?

are divisibility rules applicable here?

share|cite|improve this question
See this Math Overflow question. In your case, divisibility tells us that the difference must be $\geq$ than $$2\cdot 3\cdot 5=30.$$ – Eric Naslund Mar 22 '13 at 20:25

Yes, divisibility rules are important here. Clearly the difference must be even as all primes (except $2$) are odd. The difference must be a multiple of $3$ because otherwise two of the numbers in the progression will be multiples of $3$. Carry on. Since primes get less common as the numbers get larger, you should try starting small.

share|cite|improve this answer

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.