The 24-digit Number 357686312646216567629137

It is a fortunate and astonishing fact that the fundamental laws of our fantastic fidgety universe are based on relatively simple equations. If it were otherwise, we surely would know less than we know now about how our universe behaves, and Newton and Leibniz would probably never have invented (or discovered?) calculus.
Martin Gardner

Welcome to the blog Math1089 – Mathematics for All.

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Consider the number 357686312646216567629137. Observing the number, we can see that it is a 24-digit number. What type of natural number is it: prime or composite? In this blog post, we will consider this number.

Certainly, this is a prime number with 24 digits. Even more important is that it contains no zeros, and if we successively remove the leading left digits, then all the resulting numbers are prime. As a result, this is a left-truncable prime. More about left-truncable primes can be found here.

More conveniently, when we write the number as 3-5-7-6-8-6-3-1-2-6-4-6-2-1-6-5-6-7-6-2-9-1-3-7, truncation from the left is now more easily visible, always resulting in a prime number. Here’s a full list to visualize:

  • 357686312646216567629137 is a prime
  • 57686312646216567629137 is a prime
  • 7686312646216567629137 is a prime
  • 686312646216567629137 is a prime
  • 86312646216567629137 is a prime
  • 6312646216567629137 is a prime
  • 312646216567629137 is a prime
  • 12646216567629137 is a prime
  • 2646216567629137 is a prime
  • 646216567629137 is a prime
  • 46216567629137 is a prime
  • 6216567629137 is a prime
  • 216567629137 is a prime
  • 16567629137 is a prime
  • 6567629137 is a prime
  • 567629137 is a prime
  • 67629137 is a prime
  • 7629137 is a prime
  • 629137 is a prime
  • 29137 is a prime
  • 9137 is a prime
  • 137 is a prime
  • 37 is a prime
  • 7 is a prime

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