Frequently asked questions about primes

By Chris Caldwell

Here is a list of questions and answers for many of the frequently asked questions at this site.  If you have difficulty finding what you want, you might try searching through the site.

• The definition of prime:
  • Can negative numbers be prime?
  • Why is the number one not a prime?
  • Are all primes (other than 2 and 3) one more or less than a multiple of six?
  • Why are primes called 'prime'?
• Basic properties of primes
  • How do we prove there are infinitely many primes?
  • How many primes are there less than x?  (The answer is called pi(x).)
  • What is know about the gaps between primes?
  • Is there a formula for the nth Prime?
  • Isn't there a number A for which is always prime?
  • Does Benford's law apply to prime numbers?
• Lists and records
  • What are the first
    • 1,000 Primes? (about 7k)
    • 10,000 Primes? (about 72k)
    • 100,008 Primes? (about 822k)
    • other lists of primes
  • What is the
    • largest known prime?
    • largest known twin prime?
    • see also the Top Twenty pages
  • What is the longest list of primes?
  • Where is a list of the x-digit primes?
  • I need a few small primes (say 10 to 300 digits)
• Mersenne Numbers
  • What are the known Mersenne primes?
  • What are the decimal expansion of the Mersenne numbers? (and how do you "say" these numbers?)
  • Where is the next Mersenne prime?
• Miscellaneous
  • What is the probability that gcd(n,m)=1?
  • Why do people find these big primes?
• Questions from those who find primes:
  • How do I get a prime added to your list?
  • What is the fastest way to multiply two integers?
  • Why require passwords?
• Questions from those who have proved something new
  • I have a new result, what do I do with it?