#math trivia for #June7: #159 is the product of 3 and 53, two primes with the same last digit. What other day-numbers have this property?
— Burt Kaliski Jr. (@modulomathy) June 8, 2012
One of the primes must be less than or equal to the square root of 366, i.e., 19 or less. We can enumerate the possibilities for the other prime, and thus the product, accordingly:
- 3: 3 -> 9; 13 -> 39; 23 -> 69; 43 -> 129; 53 -> 159; 73 -> 219; 83 -> 249; 103 -> 309; 113 -> 349
- 5: 5 -> 25
- 7: 7 -> 49; 17 -> 119; 37 -> 259; 47 -> 329
- 11: 11 -> 121; 31 -> 341
- 13: 13 -> 169; 23 -> 299
- 17: 17 -> 289
It’s interesting how many of these products have primes with the last digit of 3, and how few with 5. Why is that?
modulomathy.com 