Number Recreations

What is New? (Update 3 August, 2025)

• The new 600 plus page book Exploring the Beauty of Fascinating Numbers published by SPRINGER in March 2025 is full of number curiosities, coincidences and new eye opening properties with explorable ideas, with many new and unpublished results.
  

  amazon.com
  amazon.co.uk
  amazon.co.jp
  amazon.de
  and other online book shops.

• My Book Exploring the Beauty of Fascinating Numbers published by SPRINGER was mentioned in "The Guardian" (UK) on 7th July 2025.
  
  Can you solve it? The world's most fascinating number - revealed!
  Did you solve it? The world's most fascinating number - revealed!
  

• CYF NO. 63 Contribution and Solution by Alan Zimmermann, Patrick De Geest, Mark Mammel, Oleg Vlasii, Frederic van der Plancke, and Joe Wetherell given.

• CYF NO. 62 Solution by Giorgos Kalogeropoulos given.

• CYF NO. 61 Solution by Brian Trial given.

• Prime curios 211, 284, 2992890, 14159...26433 (25-digits), and 49480...00037 (92-digits) added.

• Integer Sequences A383646, A383291, A383290, A382922, A381046, A382457, A383821, A383640, A383639, A382638, A381047, A381045, A382861, A382860, A382896, A382798, A382797, A382796, A382452, A382456, A382380, A380715, and A380713 contributed to OEIS.

• Palindromic Primes up to 10²⁵ was computed in about 3600 hours of CPU time.

• 17350-digit memorable prime discovered by me was reported in 'Spektrum der Wissenschaft' (German Science magazine) and was translated by Scientific American.

Do You Know?

4607064 is the smallest palindromic Ramanujan number i.e., the smallest palindromic number that can be expressed as the sum of two cubes in two different ways:
4607064 = 32³ + 166³ = 129³ + 135³

Can You Find?

Contents

• Rare Numbers
• EP0RNS(Equal Product Of Reversible Numbers)
• Unique Numbers
• Unlucky 13
• Fascinating Squares
• Curious Properties of 153
• Amicable Numbers (Including Happy and Harshad Amicable Pairs)
• Fascinating Triangular Numbers
• Smith Numbers
• Cab Numbers
• Fascinating Factorials
• Amazing Number 108
• The Number of Beast 666
• Vampire Numbers
• Happy numbers
• Kaprekar numbers
• Fibonacci Numbers
• Prime Polynomials
• Ramanujan Numbers

Note: The above topics including many more will be added in due course.

Prime Curios! - site maintained by G. L. Honaker Jr. and Chris Caldwell

I ranked second among the prime curios submitters in the world, with more than 1300 prime curios that list interesting things about prime numbers.

• 1 2 3 5 6 7 11 13 14 19 23 25 27 28 29 31 41 45 51 53 65 75 89 101 124 140 142 149 153
• 177 199 207 220 233 299 567 645 663 726 821 1123 1297 1973 2441 3319 4023 4201
• 5387 5879 6318 6899 10201 15841 17163 65281 29929 88357 112583 129921 135799
• 161038 189375 206483 211673 632148 656601 755968 823799 853211 864203 975313
• 1346269 1618033 2024689 2718281 4463535 15966114 19999999 118689518 123456879
• 179376463 191735161 202536181 683441871 880346227 987634512 987653214 999828727
• 1023465798 1023479856 1234457689 1608906624 3778888999 9876534120 10234465789
• 100123456789 198765432101 399899999999999 29998999999999999999999
• 16180...05887 (280-digits)

  And many more

My Favorite Links

• The Prime Puzzles and Problems Connection by Carlos Rivera has lot of interesting material related to prime numbers.

• Lots of information on prime numbers can be found at the Prime Pages.

• Prime Curios!, by G. L. Honaker, Jr. & Chris Caldwell

• Eppstein's Number Theory by David Eppstein has number of simple Number Theoretic Algorithms.

• Magic Squares,Magic Stars and Other Interesting number patterns by Harvey Heinz

• Number Theory Web by Keith Matthews

• Mudd Math Fun Facts pages

• Eric Weissteins MathWorld Encyclopedia

• On-Line Encyclopedia of Integer Sequences OEIS

• Math Puzzles
  An interesting site with lot of math recreations by Ed Pegg Jr.

• Overview of Mathematician's Secret Room
  Challenges to the Unsolved Problems in Number Theory.

• Patrick De Geest's World!Of Numbers
  All about palindromic numbers and many other number recreations.