Prime Number Checker

The checker uses trial division. It tries dividing your number by 2, 3, 4 and so on, divides out every factor it finds, and stops once the divisor squared is larger than what's left. If nothing divides the number, it's prime. You get a Yes — prime or No — composite verdict plus the full prime factorization, with repeated factors written out.

Stopping at the square root is safe because factors come in pairs. If n = a × b, one of the two is at most √n. For the default, 97, only divisors 2 to 9 need testing, since 10 × 10 = 100 is already past 97. None divides it, so 97 is prime.

91 and 221 catch people out because they're odd, don't end in 5, and have digit sums that aren't multiples of 3. The quick rules miss them, and the checker doesn't.

• 0 and 1 are reported as "No — composite" with no factorization. The "No" is right, but the label isn't: neither number is composite. 1 is neither prime nor composite, and 0 is divisible by everything.
• Negative numbers are checked without the minus sign, so −7 is reported as prime 7.
• Decimals are rounded to the nearest whole number first, so 7.4 is checked as 7. The heading shows the number actually tested, for example "Is 7 prime?".

• Ends in 0, 2, 4, 6 or 8: divisible by 2.
• Digit sum divisible by 3: divisible by 3. For 561, 5 + 6 + 1 = 12.
• Ends in 0 or 5: divisible by 5.
• Alternating digit sum divisible by 11: divisible by 11. For 1001, 1 − 0 + 0 − 1 = 0.

Every prime above 3 is one more or one less than a multiple of 6, but the reverse doesn't hold: 91 is 6 × 15 + 1 and still composite. Use these rules to rule numbers out, and the checker to confirm.

To keep the page responsive, trial division stops at divisor 10,000,000. Every number below 100 trillion (10¹⁴) is fully checked, because its square root is under that limit. Above it, a number with no factor below 10 million is reported as prime even when it isn't. For example, 100,000,980,001,501 is 10,000,019 × 10,000,079, yet the checker calls it prime.

Beyond 9,007,199,254,740,992 the browser can't store every whole number exactly, so the number tested may not even be the one you typed. For anything above 100 trillion, use a dedicated math tool.