Giving a quick inspection at the list of prime numbers, you’d notice that 2 is the first prime number. However, prepending any single decimal digit to it would not produce other primes, that is, 12, 22, 32, 42, 52, 62, 72, 82 and 92 are composite numbers. Likewise, the third prime number, 5, also shares […]

If you add all the substrings of 891, the sum is 198, which is the reverse of 891: 891 → 8 + 9 + 1 + 89 + 91 = 198 This is the only 3-digit number that has this property. There is also one 4-digit number with the same property. Can you find this […]

To the Ninth Power 59 + 39 + 49 + 49 + 99 + 49 + 89 + 39 + 69 = 534494836 Münchhausen Numbers Münchhausen number is a number equal to the sum of its nonzero digits raised to each digit’s power. There are only two of these numbers besides the trivial 0 and 1. See A046253.

Palindrome and Prime 93639 (a palindromic number) plus the sum of its prime factors is equal to 93683, which is a prime number: 93683 = 93639 + 3 + 7 + 7 + 7 + 7 + 13 Interestingly, there is no prime number between 93639 and 93683.

My previous post “Can Two 2’s Produce 5?” showed a way to produce 5 using only two 2’s and any mathematical operations. Now, here’s another similar puzzle. Using eight 8’s and any mathematical operations and symbols, can you make them equal to 1000? There are several solutions.