Prime numbers are positive integers greater than 1 that have no divisors other than 1 and themselves. In other words, a prime number is a natural number that cannot be formed by multiplying two smaller natural numbers. For example, the first few prime numbers are 2, 3, 5, 7, 11, 13, and so on. Check the complete list of prime numbers from 1 to 5000.
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Here’s a more formal definition: A positive integer p is considered prime if and only if its only positive divisors are 1 and p itself. If a positive integer n has divisors other than 1 and itself, it is called a composite number. For instance: The numbers 2 and 3 are prime numbers because its only divisors are 1 and 2 & 1 and 3 respectively. The number 4 is not a prime number because it has divisors 1, 2, and 4.
Prime numbers play a fundamental role in number theory and have applications in various fields including cryptography, computer science, and mathematics. The distribution of prime numbers is a complex topic that has fascinated mathematicians for centuries.
List of Prime Numbers (1-5000)
| S.No | Prime Number |
|---|---|
| 1 | 2 |
| 2 | 3 |
| 3 | 5 |
| 4 | 7 |
| 5 | 11 |
| 6 | 13 |
| 7 | 17 |
| 8 | 19 |
| 9 | 23 |
| 10 | 29 |
| 11 | 31 |
| 12 | 37 |
| 13 | 41 |
| 14 | 43 |
| 15 | 47 |
| 16 | 53 |
| 17 | 59 |
| 18 | 61 |
| 19 | 67 |
| 20 | 71 |
| 21 | 73 |
| 22 | 79 |
| 23 | 83 |
| 24 | 89 |
| 25 | 97 |
| 26 | 101 |
| 27 | 103 |
| 28 | 107 |
| 29 | 109 |
| 30 | 113 |
| 31 | 127 |
| 32 | 131 |
| 33 | 137 |
| 34 | 139 |
| 35 | 149 |
| 36 | 151 |
| 37 | 157 |
| 38 | 163 |
| 39 | 167 |
| 40 | 173 |
| 41 | 179 |
| 42 | 181 |
| 43 | 191 |
| 44 | 193 |
| 45 | 197 |
| 46 | 199 |
| 47 | 211 |
| 48 | 223 |
| 49 | 227 |
| 50 | 229 |
| 51 | 233 |
| 52 | 239 |
| 53 | 241 |
| 54 | 251 |
| 55 | 257 |
| 56 | 263 |
| 57 | 269 |
| 58 | 271 |
| 59 | 277 |
| 60 | 281 |
| 61 | 283 |
| 62 | 293 |
| 63 | 307 |
| 64 | 311 |
| 65 | 313 |
| 66 | 317 |
| 67 | 331 |
| 68 | 337 |
| 69 | 347 |
| 70 | 349 |
| 71 | 353 |
| 72 | 359 |
| 73 | 367 |
| 74 | 373 |
| 75 | 379 |
| 76 | 383 |
| 77 | 389 |
| 78 | 397 |
| 79 | 401 |
| 80 | 409 |
| 81 | 419 |
| 82 | 421 |
| 83 | 431 |
| 84 | 433 |
| 85 | 439 |
| 86 | 443 |
| 87 | 449 |
| 88 | 457 |
| 89 | 461 |
| 90 | 463 |
| 91 | 467 |
| 92 | 479 |
| 93 | 487 |
| 94 | 491 |
| 95 | 499 |
| 96 | 503 |
| 97 | 509 |
| 98 | 521 |
| 99 | 523 |
| 100 | 541 |
| 101 | 547 |
| 102 | 557 |
| 103 | 563 |
| 104 | 569 |
| 105 | 571 |
| 106 | 577 |
| 107 | 587 |
| 108 | 593 |
| 109 | 599 |
| 110 | 601 |
| 111 | 607 |
| 112 | 613 |
| 113 | 617 |
| 114 | 619 |
| 115 | 631 |
| 116 | 641 |
| 117 | 643 |
| 118 | 647 |
| 119 | 653 |
| 120 | 659 |
| 121 | 661 |
| 122 | 673 |
| 123 | 677 |
| 124 | 683 |
| 125 | 691 |
| 126 | 701 |
| 127 | 709 |
| 128 | 719 |
| 129 | 727 |
| 130 | 733 |
| 131 | 739 |
| 132 | 743 |
| 133 | 751 |
| 134 | 757 |
| 135 | 761 |
| 136 | 769 |
| 137 | 773 |
| 138 | 787 |
| 139 | 797 |
| 140 | 809 |
| 141 | 811 |
| 142 | 821 |
| 143 | 823 |
| 144 | 827 |
| 145 | 829 |
| 146 | 839 |
| 147 | 853 |
| 148 | 857 |
| 149 | 859 |
| 150 | 863 |
| 151 | 877 |
| 152 | 881 |
| 153 | 883 |
| 154 | 887 |
| 155 | 907 |
| 156 | 911 |
| 157 | 919 |
| 158 | 929 |
| 159 | 937 |
| 160 | 941 |
| 161 | 947 |
| 162 | 953 |
| 163 | 967 |
| 164 | 971 |
| 165 | 977 |
| 166 | 983 |
| 167 | 991 |
| 168 | 997 |
| 169 | 1009 |
| 170 | 1013 |
| 171 | 1019 |
| 172 | 1021 |
| 173 | 1031 |
| 174 | 1033 |
| 175 | 1039 |
| 176 | 1049 |
| 177 | 1051 |
| 178 | 1061 |
| 179 | 1063 |
| 180 | 1069 |
| 181 | 1087 |
| 182 | 1091 |
| 183 | 1093 |
| 184 | 1097 |
| 185 | 1103 |
| 186 | 1109 |
| 187 | 1117 |
| 188 | 1123 |
| 189 | 1129 |
| 190 | 1151 |
| 191 | 1153 |
| 192 | 1163 |
| 193 | 1171 |
| 194 | 1181 |
| 195 | 1187 |
| 196 | 1193 |
| 197 | 1201 |
| 198 | 1213 |
| 199 | 1217 |
| 200 | 1223 |
| 201 | 1229 |
| 202 | 1231 |
| 203 | 1237 |
| 204 | 1249 |
| 205 | 1259 |
| 206 | 1277 |
| 207 | 1279 |
| 208 | 1283 |
| 209 | 1289 |
| 210 | 1291 |
| 211 | 1297 |
| 212 | 1301 |
| 213 | 1303 |
| 214 | 1307 |
| 215 | 1319 |
| 216 | 1321 |
| 217 | 1327 |
| 218 | 1361 |
| 219 | 1367 |
| 220 | 1373 |
| 221 | 1381 |
| 222 | 1399 |
| 223 | 1409 |
| 224 | 1423 |
| 225 | 1427 |
| 226 | 1429 |
| 227 | 1433 |
| 228 | 1439 |
| 229 | 1447 |
| 230 | 1451 |
| 231 | 1453 |
| 232 | 1459 |
| 233 | 1471 |
| 234 | 1481 |
| 235 | 1483 |
| 236 | 1487 |
| 237 | 1489 |
| 238 | 1493 |
| 239 | 1499 |
| 240 | 1511 |
| 241 | 1523 |
| 242 | 1531 |
| 243 | 1543 |
| 244 | 1549 |
| 245 | 1553 |
| 246 | 1559 |
| 247 | 1567 |
| 248 | 1571 |
| 249 | 1579 |
| 250 | 1583 |
| 251 | 1597 |
| 252 | 1601 |
| 253 | 1607 |
| 254 | 1609 |
| 255 | 1613 |
| 256 | 1619 |
| 257 | 1621 |
| 258 | 1627 |
| 259 | 1637 |
| 260 | 1657 |
| 261 | 1663 |
| 262 | 1667 |
| 263 | 1669 |
| 264 | 1693 |
| 265 | 1697 |
| 266 | 1699 |
| 267 | 1709 |
| 268 | 1721 |
| 269 | 1723 |
| 270 | 1733 |
| 271 | 1741 |
| 272 | 1747 |
| 273 | 1753 |
| 274 | 1759 |
| 275 | 1777 |
| 276 | 1783 |
| 277 | 1787 |
| 278 | 1789 |
| 279 | 1801 |
| 280 | 1811 |
| 281 | 1823 |
| 282 | 1831 |
| 283 | 1847 |
| 284 | 1861 |
| 285 | 1867 |
| 286 | 1871 |
| 287 | 1873 |
| 288 | 1877 |
| 289 | 1879 |
| 290 | 1889 |
| 291 | 1901 |
| 292 | 1907 |
| 293 | 1913 |
| 294 | 1931 |
| 295 | 1933 |
| 296 | 1949 |
| 297 | 1951 |
| 298 | 1973 |
| 299 | 1979 |
| 300 | 1987 |
| 301 | 1993 |
| 302 | 1997 |
| 303 | 1999 |
| 304 | 2003 |
| 305 | 2011 |
| 306 | 2017 |
| 307 | 2027 |
| 308 | 2029 |
| 309 | 2039 |
| 310 | 2053 |
| 311 | 2063 |
| 312 | 2069 |
| 313 | 2081 |
| 314 | 2083 |
| 315 | 2087 |
| 316 | 2089 |
| 317 | 2099 |
| 318 | 2111 |
| 319 | 2113 |
| 320 | 2129 |
| 321 | 2131 |
| 322 | 2137 |
| 323 | 2141 |
| 324 | 2143 |
| 325 | 2153 |
| 326 | 2161 |
| 327 | 2179 |
| 328 | 2203 |
| 329 | 2207 |
| 330 | 2213 |
| 331 | 2221 |
| 332 | 2237 |
| 333 | 2239 |
| 334 | 2243 |
| 335 | 2251 |
| 336 | 2267 |
| 337 | 2269 |
| 338 | 2273 |
| 339 | 2281 |
| 340 | 2287 |
| 341 | 2293 |
| 342 | 2297 |
| 343 | 2309 |
| 344 | 2311 |
| 345 | 2333 |
| 346 | 2339 |
| 347 | 2341 |
| 348 | 2347 |
| 349 | 2351 |
| 350 | 2357 |
| 351 | 2371 |
| 352 | 2377 |
| 353 | 2381 |
| 354 | 2383 |
| 355 | 2389 |
| 356 | 2393 |
| 357 | 2399 |
| 358 | 2411 |
| 359 | 2417 |
| 360 | 2423 |
| 361 | 2437 |
| 362 | 2441 |
| 363 | 2447 |
| 364 | 2459 |
| 365 | 2467 |
| 366 | 2473 |
| 367 | 2477 |
| 368 | 2503 |
| 369 | 2521 |
| 370 | 2531 |
| 371 | 2539 |
| 372 | 2543 |
| 373 | 2549 |
| 374 | 2551 |
| 375 | 2557 |
| 376 | 2579 |
| 377 | 2591 |
| 378 | 2593 |
| 379 | 2609 |
| 380 | 2617 |
| 381 | 2621 |
| 382 | 2633 |
| 383 | 2647 |
| 384 | 2657 |
| 385 | 2659 |
| 386 | 2663 |
| 387 | 2671 |
| 388 | 2677 |
| 389 | 2683 |
| 390 | 2687 |
| 391 | 2689 |
| 392 | 2693 |
| 393 | 2699 |
| 394 | 2707 |
| 395 | 2711 |
| 396 | 2713 |
| 397 | 2719 |
| 398 | 2729 |
| 399 | 2731 |
| 400 | 2741 |
| 401 | 2749 |
| 402 | 2753 |
| 403 | 2767 |
| 404 | 2777 |
| 405 | 2789 |
| 406 | 2791 |
| 407 | 2797 |
| 408 | 2801 |
| 409 | 2803 |
| 410 | 2819 |
| 411 | 2833 |
| 412 | 2837 |
| 413 | 2843 |
| 414 | 2851 |
| 415 | 2857 |
| 416 | 2861 |
| 417 | 2879 |
| 418 | 2887 |
| 419 | 2897 |
| 420 | 2903 |
| 421 | 2909 |
| 422 | 2917 |
| 423 | 2927 |
| 424 | 2939 |
| 425 | 2953 |
| 426 | 2957 |
| 427 | 2963 |
| 428 | 2969 |
| 429 | 2971 |
| 430 | 2999 |
| 431 | 3001 |
| 432 | 3011 |
| 433 | 3019 |
| 434 | 3023 |
| 435 | 3037 |
| 436 | 3041 |
| 437 | 3049 |
| 438 | 3061 |
| 439 | 3067 |
| 440 | 3079 |
| 441 | 3083 |
| 442 | 3089 |
| 443 | 3109 |
| 444 | 3119 |
| 445 | 3121 |
| 446 | 3137 |
| 447 | 3163 |
| 448 | 3167 |
| 449 | 3169 |
| 450 | 3181 |
| 451 | 3187 |
| 452 | 3191 |
| 453 | 3203 |
| 454 | 3209 |
| 455 | 3217 |
| 456 | 3221 |
| 457 | 3229 |
| 458 | 3251 |
| 459 | 3253 |
| 460 | 3257 |
| 461 | 3259 |
| 462 | 3271 |
| 463 | 3299 |
| 464 | 3301 |
| 465 | 3307 |
| 466 | 3313 |
| 467 | 3319 |
| 468 | 3323 |
| 469 | 3329 |
| 470 | 3331 |
| 471 | 3343 |
| 472 | 3347 |
| 473 | 3359 |
| 474 | 3361 |
| 475 | 3371 |
| 476 | 3373 |
| 477 | 3389 |
| 478 | 3391 |
| 479 | 3407 |
| 480 | 3413 |
| 481 | 3433 |
| 482 | 3449 |
| 483 | 3457 |
| 484 | 3461 |
| 485 | 3463 |
| 486 | 3467 |
| 487 | 3469 |
| 488 | 3491 |
| 489 | 3499 |
| 490 | 3511 |
| 491 | 3517 |
| 492 | 3527 |
| 493 | 3529 |
| 494 | 3533 |
| 495 | 3539 |
| 496 | 3541 |
| 497 | 3547 |
| 498 | 3557 |
| 499 | 3559 |
| 500 | 3571 |
| 501 | 3581 |
| 502 | 3583 |
| 503 | 3593 |
| 504 | 3607 |
| 505 | 3613 |
| 506 | 3617 |
| 507 | 3623 |
| 508 | 3631 |
| 509 | 3637 |
| 510 | 3643 |
| 511 | 3659 |
| 512 | 3671 |
| 513 | 3673 |
| 514 | 3677 |
| 515 | 3691 |
| 516 | 3697 |
| 517 | 3701 |
| 518 | 3709 |
| 519 | 3719 |
| 520 | 3727 |
| 521 | 3733 |
| 522 | 3739 |
| 523 | 3761 |
| 524 | 3767 |
| 525 | 3769 |
| 526 | 3779 |
| 527 | 3793 |
| 528 | 3797 |
| 529 | 3803 |
| 530 | 3821 |
| 531 | 3823 |
| 532 | 3833 |
| 533 | 3847 |
| 534 | 3851 |
| 535 | 3853 |
| 536 | 3863 |
| 537 | 3877 |
| 538 | 3881 |
| 539 | 3889 |
| 540 | 3907 |
| 541 | 3911 |
| 542 | 3917 |
| 543 | 3919 |
| 544 | 3923 |
| 545 | 3929 |
| 546 | 3931 |
| 547 | 3943 |
| 548 | 3947 |
| 549 | 3967 |
| 550 | 3989 |
| 551 | 4001 |
| 552 | 4003 |
| 553 | 4007 |
| 554 | 4013 |
| 555 | 4019 |
| 556 | 4021 |
| 557 | 4027 |
| 558 | 4049 |
| 559 | 4051 |
| 560 | 4057 |
| 561 | 4073 |
| 562 | 4079 |
| 563 | 4091 |
| 564 | 4093 |
| 565 | 4099 |
| 566 | 4111 |
| 567 | 4127 |
| 568 | 4129 |
| 569 | 4133 |
| 570 | 4139 |
| 571 | 4153 |
| 572 | 4157 |
| 573 | 4159 |
| 574 | 4177 |
| 575 | 4201 |
| 576 | 4211 |
| 577 | 4217 |
| 578 | 4219 |
| 579 | 4229 |
| 580 | 4231 |
| 581 | 4241 |
| 582 | 4243 |
| 583 | 4253 |
| 584 | 4259 |
| 585 | 4261 |
| 586 | 4271 |
| 587 | 4273 |
| 588 | 4283 |
| 589 | 4289 |
| 590 | 4297 |
| 591 | 4327 |
| 592 | 4337 |
| 593 | 4339 |
| 594 | 4349 |
| 595 | 4357 |
| 596 | 4363 |
| 597 | 4373 |
| 598 | 4391 |
| 599 | 4397 |
| 600 | 4409 |
| 601 | 4421 |
| 602 | 4423 |
| 603 | 4441 |
| 604 | 4447 |
| 605 | 4451 |
| 606 | 4457 |
| 607 | 4463 |
| 608 | 4481 |
| 609 | 4483 |
| 610 | 4493 |
| 611 | 4507 |
| 612 | 4513 |
| 613 | 4517 |
| 614 | 4519 |
| 615 | 4523 |
| 616 | 4547 |
| 617 | 4549 |
| 618 | 4561 |
| 619 | 4567 |
| 620 | 4583 |
| 621 | 4591 |
| 622 | 4597 |
| 623 | 4603 |
| 624 | 4621 |
| 625 | 4637 |
| 626 | 4639 |
| 627 | 4643 |
| 628 | 4649 |
| 629 | 4651 |
| 630 | 4657 |
| 631 | 4663 |
| 632 | 4673 |
| 633 | 4679 |
| 634 | 4691 |
| 635 | 4703 |
| 636 | 4721 |
| 637 | 4723 |
| 638 | 4729 |
| 639 | 4733 |
| 640 | 4751 |
| 641 | 4759 |
| 642 | 4783 |
| 643 | 4787 |
| 644 | 4789 |
| 645 | 4793 |
| 646 | 4799 |
| 647 | 4801 |
| 648 | 4813 |
| 649 | 4817 |
| 650 | 4831 |
| 651 | 4861 |
| 652 | 4871 |
| 653 | 4877 |
| 654 | 4889 |
| 655 | 4903 |
| 656 | 4909 |
| 657 | 4919 |
| 658 | 4931 |
| 659 | 4933 |
| 660 | 4937 |
| 661 | 4943 |
| 662 | 4951 |
| 663 | 4957 |
| 664 | 4967 |
| 665 | 4969 |
| 666 | 4973 |
| 667 | 4987 |
| 668 | 4993 |
| 669 | 4999 |
There are 669 prime numbers between 1 to 5000 and 2 is the first prime number. Why is 1 not a prime number? 1 is not a prime number because it has only one factor, namely 1.
Also Read: Perfect Squares List
Specialty of Prime Numbers
- Uniqueness: Every positive integer greater than 1 can be uniquely expressed as a product of prime numbers, up to the order of the factors. This is known as the Fundamental Theorem of Arithmetic.
- Infinitude of Primes: There are infinitely many prime numbers. This was proven by the ancient Greek mathematician Euclid around 300 BCE. His proof is a classic example of a proof by contradiction.
- Prime Factorization: Finding the prime factorization of a number involves breaking down that number into a product of prime factors. This process is essential in many mathematical operations, including simplifying fractions and finding the greatest common divisor (GCD) of two numbers.
- Twin Primes: Twin primes are pairs of prime numbers that have a difference of 2. For example, (3, 5), (11, 13), and (17, 19) are twin prime pairs. The Twin Prime Conjecture proposes that there are infinitely many twin prime pairs, but this has not been proven yet.
Prime Number Theorem: The Prime Number Theorem, formulated by mathematicians like Jacques Hadamard and Charles Jean de la Vallée-Poussin, describes the asymptotic distribution of prime numbers. It gives an estimate of how the density of prime numbers decreases as numbers get larger. - Prime Numbers and Cryptography: Prime numbers are crucial in modern cryptography. Public-key cryptography algorithms like RSA rely on the difficulty of factoring the product of two large prime numbers. This forms the basis of secure communication over the internet.
- Mersenne Primes: Mersenne primes are prime numbers that can be written in the form 2p – 1 where p is also a prime number. These primes have an intriguing connection to perfect numbers and are often studied for their mathematical properties.
- Prime Sieves: Prime sieves are algorithms designed to efficiently find all prime numbers up to a certain limit. The Sieve of Eratosthenes is one of the most well-known prime sieves, and it’s a simple method for identifying primes.
- Prime Gap: The prime gap refers to the difference between consecutive prime numbers. While the prime distribution seems somewhat random, there are still open questions about how large prime gaps can be.
- Prime Number Patterns: While prime numbers themselves don’t follow a predictable pattern (a property known as the “randomness” of primes), there are some patterns and conjectures related to their distribution. However, proving these conjectures remains a challenge.
Also Read: Perfect Cubes List
Prime numbers remain a rich area of study in mathematics, and they continue to captivate mathematicians and researchers around the world due to their unique properties and implications in various fields.
