๐Ÿ”ข Prime Number Checker

Discover if your number is Prime or Composite โ€“ fast and easy!

Number: 3491

โœ… Yes! It's a Prime Number

Prime numbers are only divisible by 1 and itself.

โฌ… Previous Prime: 3469 Next Prime: 3499 โžก

๐Ÿง  Did You Know?

  • 2 is the smallest and only even prime number.
  • Prime numbers play a key role in cryptography.
  • Every number is either prime, composite, or 1.
  • There are infinitely many prime numbers.
  • Mathematicians use prime numbers in advanced theories.

๐ŸŽฏ Prime Number Database

Explore comprehensive data about prime numbers and their fascinating properties.

๐Ÿ”ข 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 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541

Click any prime to analyze it!

๐Ÿ“ 25 Prime Numbers Near 3491

3373 3389 3391 3407 3413 3433 3449 3457 3461 3463 3467 3469 3491 3499 3511 3517 3527 3529 3533 3539 3541 3547 3557 3559 3571

๐Ÿ“ˆ Prime Gaps Analysis Around 3491

Twin Primes (Gap = 2)

3389โ€“3391, 3461โ€“3463, 3467โ€“3469, 3527โ€“3529, 3539โ€“3541, 3557โ€“3559 ...

Cousin Primes (Gap = 4)

3457โ€“3461, 3463โ€“3467, 3529โ€“3533 ...

Gap-6 Primes

3407โ€“3413, 3511โ€“3517, 3533โ€“3539, 3541โ€“3547 ...

๐ŸŒŸ Mersenne Primes

Primes of the form 2โฟ - 1 less than 3491

M2 = 3 (n=2)
M3 = 7 (n=3)
M5 = 31 (n=5)
M7 = 127 (n=7)

๐ŸŽญ Palindromic Primes

Primes that read the same forwards and backwards

2
3
5
7
11
101
131
151
181
191
313
353

๐Ÿ”„ Circular Primes

Primes that remain prime when digits are rotated (below 3491)

2 (single digit)
3 (single digit)
5 (single digit)
7 (single digit)
11 โ†’ 11, 11
13 โ†’ 13, 31
17 โ†’ 17, 71
31 โ†’ 31, 13
37 โ†’ 37, 73
71 โ†’ 71, 17
73 โ†’ 73, 37
79 โ†’ 79, 97
97 โ†’ 97, 79
113 โ†’ 113, 131, 311
131 โ†’ 131, 311, 113
197 โ†’ 197, 971, 719
199 โ†’ 199, 991, 919
311 โ†’ 311, 113, 131
337 โ†’ 337, 373, 733
373 โ†’ 373, 733, 337
719 โ†’ 719, 197, 971
733 โ†’ 733, 337, 373
919 โ†’ 919, 199, 991
971 โ†’ 971, 719, 197
991 โ†’ 991, 919, 199
1193 โ†’ 1193, 1931, 9311, 3119
1931 โ†’ 1931, 9311, 3119, 1193
3119 โ†’ 3119, 1193, 1931, 9311

๐Ÿ”ข Understanding Prime Numbers

Prime numbers are the building blocks of mathematics, encryption, and more. Explore what makes them fascinating.

What is a Prime Number?

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Prime numbers cannot be formed by multiplying two smaller natural numbers. The first few are: 2, 3, 5, 7, 11, 13, 17, 19, 23...

๐ŸŒ Real-World Uses

  • ๐Ÿ” RSA Encryption: Internet security
  • ๐Ÿ“ฑ Blockchain: Bitcoin mining
  • ๐ŸŽฒ Random Numbers: Gaming algorithms
  • ๐Ÿ’ป Hash Tables: Database optimization
  • ๐Ÿ›ก๏ธ Digital Signatures: Authentication
  • ๐Ÿ“ก Error Detection: Data transmission

๐Ÿงฎ Math Properties

  • 2 is the only even prime
  • All primes >3 are 6kยฑ1
  • Infinite quantity (Euclid's proof)
  • Fundamental Theorem of Arithmetic
  • Prime Number Theorem (density)
  • Goldbach's Conjecture

๐Ÿ“š Historical Facts

  • ๐Ÿ›๏ธ Known since ancient Greeks
  • ๐Ÿ“œ Sieve of Eratosthenes (276 BC)
  • ๐Ÿง  Fermat's Little Theorem (1640)
  • ๐ŸŽฏ Euler's work on primes (1700s)
  • ๐Ÿ† Riemann Hypothesis (1859)
  • ๐Ÿ’ฐ $1M Clay Prize problems

๐Ÿ† Modern Records

  • ๐Ÿฅ‡ Largest: 2โธยฒ,โตโธโน,โนยณยณ - 1
  • ๐Ÿ“ 24,862,048 digits long
  • ๐Ÿ–ฅ๏ธ Found by GIMPS project
  • โšก Distributed computing
  • ๐ŸŽ–๏ธ $150,000 prize awarded
  • ๐Ÿ” Search continues daily

๐ŸŽ“ Advanced Concepts

Prime Number Theorem

ฯ€(n) โ‰ˆ n/ln(n) - The density of primes decreases logarithmically

Riemann Hypothesis

ฮถ(s) = 0 only at s = -2,-4,-6... and Re(s) = 1/2

Bertrand's Postulate

For n > 1, there's always a prime between n and 2n

๐Ÿ”ฌ Testing Algorithms

Trial Division

Test divisibility up to โˆšn - Simple but slow O(โˆšn)

Miller-Rabin

Probabilistic test - Fast O(k logยณ n) with k rounds