Burt Kaliski Jr. (@modulomathy)
4/6/12 9:42 AM
#math trivia for #April6: #97 is the largest prime less than 100. Are primes more likely than average to occur very close to a power of 10?
“Average” here can be understood to refer to the probability that a random number “in the vicinity” (but not necessarily “very close”) to a given number is prime.
Intuitively, it seems that numbers very close to a power of 10 — or in fact, a power of any number — should be more likely to be prime, because we know, a priori, that they’re not divisible by the number, ruling out one of the possible reasons for not being prime. (We can take a difference of 3 from a power of 10 as an illustration of “very close” and assume that a difference of 10 is too far, and a difference of 0 isn’t allowed.)
In a similar way, odd numbers are more likely to be prime than random numbers, because random numbers also include even numbers, which can’t be prime (other than 2).
I’m not sure how I’d prove this, however.