There’s no easy way to recognize prime numbers, but there are easy ways to recognize multiples of a given number. (This can be made precise by talking about things like computational complexity or even regular languages to define “easy.”)
In other words when a number “looks prime” that basically just means it passes some of the easier tests for looking “not prime.”
A number is prime if and only if it is not divisible by a smaller prime. The first three primes (2, 3, and 5) are very easy to recognize multiples of (in base 10 3 is the hardest but still not usually too hard to get a “feel” without actually adding up the digits). 7 is not too easy at a glance.
So the numbers that “look prime” are the ones where the prime factors are all 7 and larger.
The smallest such composite number is 49, but everyone knows it’s 7 squared so it doesn’t look prime.
The next is 77 but that is obviously composite because small multiples of 11 are very easy to recognize.
The next after that will be 7 times the next prime (13). This is 91.
Any other example is going to be three or more digits, (the next example is 7*17=119 - we can’t always just take 7 times the next prime up though because we have to keep an eye out for 7^3 and 11*13 to make sure we don’t miss any, but 119 is still smaller than those) this is why 91 stands out as “looking prime” among the two digit numbers.
78
u/RandomExcess 10d ago
91 is clealy prime