Prime Number Calculator

Check if a number is prime, find all primes up to N, or discover prime factors. Learn about the Sieve of Eratosthenes and explore the fascinating world of prime numbers.

Prime Calculator

Select a mode and enter a number to calculate

First 100 Prime Numbers (Reference)

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
233
239
241
251
257
263
269
271
277
281
283
293
307
311
313
317
331
337
347
349
353
359
367
373
379
383
389
397
401
409
419
421
431
433
439
443
449
457
461
463
467
479
487
491
499
503
509
521
523
541

About Prime Numbers

Prime numbers are the building blocks of all natural numbers. They have fascinated mathematicians for thousands of years and play a crucial role in modern mathematics, cryptography, and computer science.

What Makes a Number Prime?

A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. The first prime is 2 (the only even prime), followed by 3, 5, 7, 11, 13, and so on.

Prime Testing Methods

  • Trial Division: Test divisibility up to √n for efficiency
  • Sieve of Eratosthenes: Find all primes up to a limit efficiently
  • Miller-Rabin: Probabilistic test for very large numbers
  • AKS Algorithm: Deterministic polynomial-time primality test

Applications of Prime Numbers

  • Cryptography: RSA encryption relies on the difficulty of factoring large primes
  • Hash Tables: Prime-sized tables reduce collisions in computer science
  • Random Number Generation: Primes help create better pseudo-random sequences
  • Cicada Life Cycles: Some cicadas emerge in prime-year cycles (13, 17 years)
  • Error Detection: Prime-based checksums in data transmission

Prime Number FAQs

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What Our Users Say

5.0
Based on 2,147 reviews

Excellent tool for teaching number theory! The step-by-step prime checking algorithm helps students understand the concept deeply. The Sieve of Eratosthenes visualization is particularly valuable. I use this in my discrete mathematics course regularly.

P
Professor James Mitchell
Mathematics Department
October 11, 2024

Perfect for my cryptography studies. The prime factorization feature helps me understand RSA encryption better. Being able to check large numbers for primality and see the step-by-step process is incredibly useful for learning.

S
Sophie Anderson
Cryptography Student
September 29, 2024

I love playing with prime numbers and this calculator makes it so easy! Finding all primes up to a given number, checking if numbers are prime, and factoring numbers - all in one place. The historical context about Eratosthenes is a nice touch too!

M
Marcus Lee
Math Enthusiast
October 6, 2024

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