My favourite prime checking algorithm is that for n < 100 if it looks prime, it is prime.

freehorse 13 hours ago | parent | next [-]

Up to 100 it is relatively simple, if you remove the even numbers, the multiples of 3 (summing up their digits recursively gives 3 6 or 9), and those that end at 5, you end up with 25 numbers out of which 22 (88%) are primes. If you further exclude 49 which you should remember is 7^2 from the multiplication table, and 77 that is obviously divisible by 7, you are left with 22/23 chance a number that passes these exclusion criteria is not 91 and hence it is a prime.

▲

jeffbee 12 hours ago | parent [-]

> summing up their digits recursively gives 3 6 or 9

What does this part mean? For example 57.

▲

zdimension 12 hours ago | parent | next [-]

57 is 3 times 19.

The standard divisibility rule for 3, 6 and 9 in base 10 is to sum the digits until you only have one left and check if it's one of those. Here, 5+7=12, 1+2=3, so 57 is divisible by 3.

▲

squigz 3 hours ago | parent | next [-]

Math is not my strong suit at all, so I probably won't grok this, but that kind of blows my mind, so I'm curious... how?! That works for any arbitrarily large number?

Math is crazy!... still don't want to study it though!

	▲	moring 2 hours ago \| parent \| next [-]
		Yes. A number like 123456 = 1 * 100000 + 2 * 10000 + 3 * 1000 + 4 * 100 + 5 * 10 + 6 = 1 * (99999+1) + 2 * (9999+1) + 3 * (999+1) + 4 * (99+1) + 5 * (9+1) + 6 When checking whether it is a multiple of some k, you can add/subtract multiples of k without changing the result, and those 99...9 are multiples of both 3 and 9. So 123456 is a multiple of 3 (or 9) iff 1 * 1 + 2 * 1 + 3 * 1 + 4 * 1 + 5 * 1 + 6 * 1 = 1 + 2 + 3 + 4 + 5 + 6 is. Apply the same rule as often as you want -- that is, until you only have one digit left, because then it won't get simpler anymore.
	▲	an hour ago \| parent \| prev [-]
		[deleted]

▲

jeffbee 12 hours ago | parent | prev [-]

Ah I see what is meant by recursively here. Thanks!

▲

hollerith 12 hours ago | parent | prev [-]

5 plus 7 is 12, which of course has a 1 and a 2, the sum of which is 3.

▲

throwaway81523 15 hours ago | parent | prev | next [-]

Like the famous Grothendieck prime of course.

	▲	xorbax 15 hours ago \| parent [-]
		Definitely makes me feel better about my own work

▲

floydian10 3 hours ago | parent | prev | next [-]

91 should be prime, ridiculous that it isn't

▲

emaccumber 15 hours ago | parent | prev | next [-]

The annoying child in me will always remember correcting my freshman math teacher when he needed a prime number and wrote 91 on the chalkboard.

▲

GMoromisato 14 hours ago | parent | prev | next [-]

Are there any numbers that don't look prime but are, in fact, prime? [Other than 2, I suppose.]

▲

andruby 14 hours ago | parent [-]

11, 13, 17 and 19 used to trip me up. And maybe 67

▲

mootothemax 10 hours ago | parent [-]

67 has absolutely no right to be prime. Sitting there looking all innocent.

	▲	bombcar 29 minutes ago \| parent [-]
		Maybe that’s the real secret behind the 6-7 meme going around

▲

ridiculous_fish 13 hours ago | parent | prev | next [-]

Except 91.

▲

conradev 13 hours ago | parent | prev | next [-]

This only works if you know multiplication tables which is not a given in America these days.

	▲	gosub100 12 hours ago \| parent [-]
		"not given" != "not able to learn"

▲

14 hours ago | parent | prev | next [-]

[deleted]

▲

wbl 9 hours ago | parent | prev [-]