Burt Kaliski Jr. (@modulomathy)
3/10/12 2:27 PM
#math trivia for #March10: #70 is one of three tricomposites this month (products of three distinct primes). What are the other two?
The three prime factors of 70 are, of course, 2, 5, and 7.
March’s day-numbers range from 60 to 91. The other tricomposites among them are
— 66 = 2 * 3 * 11
— 78 = 2 * 3 * 13
These could be determined by trial and error, looking at each day-number in the range, or by construction. With the latter method, we’d look at multiples of 2*3=6 and a larger prime that fall in the range (only 66 and 78 do, as already indicated); then of 2*5=10 (just the one in the problem statement), and 3*5=15 (none). (Other pairs of primes, when multiplied by a yet larger prime, exceed the range.)
There a few near misses in the range. 63, 68, 75 and 76 are both products of three primes, but they’re not all distinct. 60 has three distinct prime factors, but it’s not a tricomposite, i.e., not the product of the three distinct primes — one of the factors is repeated.