Quickly test if a number is prime or find its prime factorization. Essential for math students, cryptography enthusiasts, and number theory applications.

About Prime Numbers

Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves. They are fundamental in mathematics with critical applications in cryptography, computer science, and number theory.

How to Use This Calculator

Enter a positive integer in the input field (max 15 digits)
Click "Test Prime" to check primality or "Factorize" to see prime factors
Results appear instantly with factorization steps and visual tree

Examples

123456789 = 3² × 3607 × 3803
987654321 = 3² × 17² × 379721
104729 is prime (the 10,000th prime number)

First 100 Prime Numbers

2	3	5	7	11	13	17	19	23	29
31	37	41	43	47	53	59	61	67	71
73	79	83	89	97	101	103	107	109	113
127	131	137	139	149	151	157	163	167	173
179	181	191	193	197	199	211	223	227	229

Important Notes

1 is not considered a prime number
2 is the only even prime number
Large numbers may take longer to factorize (trial division up to √n)
Very large numbers (>10¹²) may face browser performance limits

Prime Number Calculator

Calculator

Factor Tree Visualization

About Prime Numbers

How to Use This Calculator

Examples

First 100 Prime Numbers

Important Notes

FAQ

What is the largest number this can factor?

How accurate is the prime test?

Why does 1 show as not prime?

Disclaimer

References

2	3	5	7	11	13	17	19	23	29
31	37	41	43	47	53	59	61	67	71
73	79	83	89	97	101	103	107	109	113
127	131	137	139	149	151	157	163	167	173
179	181	191	193	197	199	211	223	227	229

2	3	5	7	11	13	17	19	23	29
31	37	41	43	47	53	59	61	67	71
73	79	83	89	97	101	103	107	109	113
127	131	137	139	149	151	157	163	167	173
179	181	191	193	197	199	211	223	227	229

2	3	5	7	11	13	17	19	23	29
31	37	41	43	47	53	59	61	67	71
73	79	83	89	97	101	103	107	109	113
127	131	137	139	149	151	157	163	167	173
179	181	191	193	197	199	211	223	227	229

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Prime Number Calculator - Test or Factor Quickly

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