Prime Number Checker

Type any whole number from one upward and this checker says whether it is prime as you type, lists every factor it has, and names the nearest primes above and below.

What is the Prime Number Checker?

A prime number is a whole number greater than 1 whose only divisors are 1 and itself, so 7 is prime while 9 is not, because 3 divides it evenly. This checker settles that question for a number you type by ruling out 2 and 3 first, then testing candidate divisors of the form 6k plus or minus 1 until the candidate exceeds the square root of your number. Alongside the verdict it shows the complete set of divisors, the digit sum, and the closest prime on either side.

Key Features

• Trial division skips multiples of 2 and 3, stopping at the square root
• Every divisor listed in ascending order, with the total factor count
• Nearest prime above and nearest prime below the number you entered
• Digit sum shown, which doubles as a divisibility-by-3 test
• Six preset buttons, from 2 up to the prime 1000000007

Common Use Cases

• Checking factor and prime-factorization homework in middle school or early algebra
• Picking a prime modulus for hashing or competitive programming, such as 1000000007
• Testing whether a year, ID, or serial number happens to be prime
• Exploring twin primes and prime gaps by stepping through consecutive values

How to Use the Prime Number Checker

1. Type a whole number into the Enter a Number field; the page recalculates on every keystroke.
2. Read the verdict panel: a green check means prime, a red cross means composite.
3. Read the line under the verdict for the exact number of factors found.
4. Compare the four info cards: factor count, next prime, previous prime, and sum of digits.
5. Scroll to the Factors list for every divisor, or tap a preset such as 7919 or 1000000007.

Tips for Best Results

• If the digit sum is divisible by 3, the number is too, so it cannot be prime unless it is 3.
• A factor count of exactly 2 always means prime; 1 shows a count of 1 and is therefore not prime.
• Decimals are truncated to whole numbers, and anything below 1 snaps back to 1.
• Past a few billion the divisor scan slows, since it tests every integer up to the square root.

Why Use WiserWork's Prime Number Checker?

Ordinary calculators give you a quotient, not a verdict, and hand-testing divisors past three or four digits is slow and easy to get wrong. This page does the divisibility work and then shows its evidence, the full divisor list, the factor count and the neighboring primes, so you can check the reasoning instead of trusting a bare yes or no. Everything is computed in your browser with standard JavaScript integers, which stay exact up to 9007199254740991.

Who Uses the Prime Number Checker?

Students working through factors, divisibility rules and prime factorization use it to verify answers they worked out on paper. Programmers reach for it when choosing a prime modulus or sanity-checking a constant, and puzzle solvers use the next-prime and previous-prime cards to hunt for twin primes and unusually long prime gaps. Teachers find the visible factor list useful for showing why a number fails the test rather than just announcing that it does.

Frequently Asked Questions

Why is 1 not a prime number?

A prime has exactly two distinct divisors, 1 and itself, and 1 has only one divisor. Enter 1 here and the factor count card reads 1, which is why the verdict comes back not prime. Treating 1 as prime would also break unique factorization, since you could pad any factorization with as many 1s as you liked.

Why is 2 the only even prime?

Every even number is divisible by 2, so any even number larger than 2 has at least three divisors: 1, 2 and itself. That leaves 2 as the only even number with exactly two divisors. The checker relies on this and discards even candidates immediately.

What algorithm does this checker use?

It uses trial division with a 6k plus or minus 1 wheel: numbers below 2 are rejected, 2 and 3 are accepted, multiples of 2 or 3 are discarded, and then it tests 5, 7, 11, 13, 17, 19 and so on. It stops as soon as the candidate divisor squared exceeds the number.

Why is it enough to test divisors only up to the square root?

If a number n factors as a times b, one of those two factors must be at most the square root of n, because if both were larger their product would exceed n. So any composite number is guaranteed to reveal a divisor at or below its square root, and finding none proves it is prime.

What is the largest number I can check?

The arithmetic stays exact up to 9007199254740991, the largest integer JavaScript represents without rounding, since the page uses ordinary numbers rather than BigInt. In practice it stays responsive into the billions, and the 1000000007 preset returns immediately. Well beyond that the divisor scan, which visits every integer up to the square root, starts to lag as you type.

Are the numbers in the Factors list the prime factorization?

No, that list contains every divisor, not just the prime ones. Enter 12 and you get 1, 2, 3, 4, 6 and 12, whereas the prime factorization of 12 is 2 times 2 times 3. You can spot the prime factors within the list by checking each entry.

What do the four info cards show?

Number of Factors is the count of all divisors, so 2 means prime. Next Prime and Previous Prime are the closest primes above and below your number, found by stepping one integer at a time. Sum of Digits adds the decimal digits, which is handy for divisibility rules.

Why does Previous Prime show a dash for 1 and 2?

2 is the smallest prime, so there is no prime below it and none below 1 either. The card shows a dash rather than a misleading number in those two cases.

What happens if I enter a decimal, zero, or a negative number?

Decimals are truncated to the whole number part, so 9.7 is checked as 9. The field has a minimum of 1, and any value below 1, including 0 and negatives, is treated as 1. Primality is defined only for whole numbers greater than 1 anyway.

Is this the kind of primality test used in cryptography?

No. RSA and similar systems use primes hundreds of digits long, and trial division would take longer than the age of the universe on numbers that size, so they rely on probabilistic tests such as Miller-Rabin. Their security rests on the fact that multiplying two big primes is easy while factoring the product is not, which is the same asymmetry you see here when a large composite reveals its divisor almost at once.

From single digits up to the ten-digit presets, this checker gives you a verdict plus the working behind it: every divisor, the factor count, the digit sum, and the primes sitting immediately above and below.