# The largest Friday number

A Friday number is a prime number N where any three consecutive digits make a prime, and all such primes formed are distinct.

For example, 1373 is a Friday number because 137, 373 and 1373 are all distinct primes.

Find the largest Friday number.

• Credits: @TimCouwelier – ghosts_in_the_code Sep 30 '15 at 12:22
• @GordonK No, now the entire number has to be a prime as well. – ghosts_in_the_code Sep 30 '15 at 12:23
• lol, you are two days ahead now. Maybe an idea for the next number question: What's the largest $n$-digit prime number where any $n-1$,$n-2$,...,$3$ and $2$ consecutive digits make a prime. – Ivo Beckers Sep 30 '15 at 12:35
• Are leading zeroes allowed? (For example, is 1013 a Friday number?) – r3mainer Sep 30 '15 at 13:14
• Might be a good idea too make even more obvious the difference with your Thursday number question. I nearly voted down because I didn't notice (even though italicized) the Thursday number didn't need to be prime (so it was an obscure variant of your previous question). However, your question really is simply - Whats the largest prime 'Thursday number' really. – Spacemonkey Sep 30 '15 at 14:40

9419919379719113739773313173

Using the primes

941 419 199 991 919 193 937 379 797 971 719 171 911 113 137 373 739 397 977 773 733 331 313 131 317 173

When attempting to solve the Thursday number, I ended up with a list of 260 groups of 24 3-digit primes, where all primes only contained 1, 3, 7, and 9.

All 260 numbers in my list start with a 1. All also contain 971 and 991. That led me to finding the largest one that was a prime with 94 added to the beginning.

Working from the 260th (largest) backwards, the 250th was the first one to be a prime with 94 added to the start of it.

• How did you confirm the resulting number to be prime? – Tim Couwelier Oct 1 '15 at 10:48
• I just googled the numbers. Once I got to this number, multiple sites listed it. – Joel Rondeau Oct 1 '15 at 11:25
• Turns out, once you have that, primepuzzles.net/puzzles/puzz_253.htm is a rather interesting page. It also shows solutions for 4 digit- and 5 digit-primes. Surprisingly, the numbers increase drastically by pushing up the length of the individual primes... – Tim Couwelier Oct 1 '15 at 13:52
• The site that made me satisfied that I'd solved it was primes.utm.edu/curios/page.php?number_id=4022 – Joel Rondeau Oct 1 '15 at 13:55