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Burt Kaliski Jr. (@modulomathy) 3/27/12 7:44 AM #math trivia for #March27: #87 is three times a prime. How many numbers of this form this year? (As usual, looking at numbers 1-366.) This time it’s the number of primes up to 122: π(122) = 30.

Burt Kaliski Jr. (@modulomathy) 3/26/12 8:55 AM #math trivia for #March26: #86 is two times a prime. How often does this happen in a leap year? (Including 2*2=4.) The equivalent question is, how many primes are between 1 and 183? This value is denoted π(183), the number of primes less than or equal to 183. … Continue reading →

Burt Kaliski Jr. (@modulomathy) 3/25/12 10:28 AM #math trivia for #March25: #85 is 55 base 16. How many “two of a kinds” base 16 in a leap year? (Compare #66.) “Two of a kind” means that two of the digits are the same, base 16. This happens 15 times from 11 to ff base 16, … Continue reading →

Burt Kaliski Jr. (@modulomathy) 3/24/12 10:06 AM #math trivia for #March24: #84 is 2^2*3*7. How many divisors does it have and why? Compare solution to #42: wp.me/p2ef3C-f There are 12 divisors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84. Here’s why the number is 12: Each divisor must … Continue reading →

Burt Kaliski Jr. (@modulomathy) 3/23/12 11:49 AM #math trivia for #March23: #83 has a “signature” of (1,2,3,6) modulo the primes (2,3,5,7). What’s the next number with this signature? Because 2, 3, 5 and 7 are distinct primes (pairwise relatively prime would be sufficient), the signature repeats with a period equal to the product of the … Continue reading →

Burt Kaliski Jr. (@modulomathy) 3/21/12 2:54 PM #math trivia for #March21: #81 is a square, and the sum of its digits is a square. What other days this year have this property? The one-digit squares all have this property: 1, 4, 9. Among the 15 other day-numbers not already mentioned that are squares, the ones … Continue reading →

Burt Kaliski Jr. (@modulomathy) 3/20/12 11:06 AM #math trivia for #March20: #80 has the form x^4-1 for x > 2 so must have at least three nontrivial divisors. What are they, and why three? The nontrivial divisors of 80 (those other than 80 or 1) are 2, 4, 5. 8, 10, 16, 20, and 40. … Continue reading →

Burt Kaliski Jr. (@modulomathy) 3/19/12 10:37 PM #math trivia for #March19: #79 has one of the highest digit sums of any two-digit prime: 7+9=16. Which two-digit prime has a higher sum? The only two-digit prime with a higher digit sum than 79 is 89. Indeed, the only two-digit numbers with a higher digit sum than … Continue reading →