− This page indexes many of the lists of primes stored at this site. 12n+1: 13, 37, 61, 73, 97, 109, 157, 181, 193, 229, 241, 277, 313, 337, 349 (OEIS: A068228) Why such page ? The first 10 million prime numbers. This Java program allows the user to enter any integer value. For n ≥ 2, write the prime factorization of n in base 10 and concatenate the factors; iterate until a prime is reached. A prime 3, 5, 7, 31, 53, 97, 211, 233, 277, 367, 389, 457, 479, 547, 569, 613, 659, 727, 839, 883, 929, 1021, 1087, 1109, 1223, 1289, 1447, 1559, 1627, 1693, 1783, 1873 (OEIS: A006378), (5, 11), (7, 13), (11, 17), (13, 19), (17, 23), (23, 29), (31, 37), (37, 43), (41, 47), (47, 53), (53, 59), (61, 67), (67, 73), (73, 79), (83, 89), (97, 103), (101, 107), (103, 109), (107, 113), (131, 137), (151, 157), (157, 163), (167, 173), (173, 179), (191, 197), (193, 199) (OEIS: A023201, OEIS: A046117). For example 2, 3, 5, 7…are prime numbers. Eisenstein integers that are irreducible and real numbers (primes of the form 3n − 1). n {\displaystyle 0\leq a\pm b<10} There are known formulae to evaluate the prime-counting function (the number of primes below a given value) faster than computing the primes. And the last is a printable list of the first 100 prime numbers to use in a binder or as a Math poster, etc. For other small a, they are given below: a = 3: 13, 1093, 797161, 3754733257489862401973357979128773, 6957596529882152968992225251835887181478451547013 (OEIS: A076481), a = 5: 31, 19531, 12207031, 305175781, 177635683940025046467781066894531, 14693679385278593849609206715278070972733319459651094018859396328480215743184089660644531 (OEIS: A086122), a = 6: 7, 43, 55987, 7369130657357778596659, 3546245297457217493590449191748546458005595187661976371 (OEIS: A165210), a = 7: 2801, 16148168401, 85053461164796801949539541639542805770666392330682673302530819774105141531698707146930307290253537320447270457. But factors of 7 are only 1 and 7, totally two. Partition function values that are prime. Next we test 4. Pn = 2Pn−1 + Pn−2. 121021, 121151, 150151, 151051, 151121, 180181, 180811, 181081 (OEIS: A134996). y ( 2p − 1 ≡ 1 (mod p2): 1093, 3511 (OEIS: A001220) 2 2, 3, 5, 7, 23, 29, 31, 37, 53, 59, 71, 73, 79, 233, 239, 293, 311, 313, 317, 373, 379, 593, 599, 719, 733, 739, 797, 2333, 2339, 2393, 2399, 2939, 3119, 3137, 3733, 3739, 3793, 3797 (OEIS: A024770). 557.935 is an average of first 200 prime numbers mentioned in the below table, by substituting the total sum and count of numbers in the formula. 7, 13, 97, 193, 769, 12289, 786433, 3221225473, 206158430209, 6597069766657 (OEIS: A039687). A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. 1 a The main list we keep is the list of the 5000 largest known primes and selected smaller primes. Some sequences have alternate names: 4n+1 are Pythagorean primes, 4n+3 are the integer Gaussian primes, and 6n+5 are the Eisenstein primes (with 2 omitted). 2, 5, 877, 27644437, 35742549198872617291353508656626642567, 359334085968622831041960188598043661065388726959079837. Finally, the prime number generator even gives you the option to create a printer-friendly prime numbers chart containing your custom list. ± Example: 5 can be factorized in only one way, that is, 1 × 5 (OR) 5 × 1. The number 6 is not a prime number because it is possible to express it as a product of prime factors. 1 We also have a glossary, top 10 records lists, prime-music, programs, free downloads, and much more! ; Start with the first and the smallest prime number 2. 6p − 1 ≡ 1 (mod p2): 66161, 534851, 3152573 (OEIS: A212583) A prime number is one that is only divisible by 1 and itself. Primes that remain prime when the leading decimal digit is successively removed. The first 1000 primes are listed below, followed by lists of notable types of prime numbers in alphabetical order, giving their respective first terms. Find the multiples of p i.e. ( Prime elements of the Gaussian integers; equivalently, primes of the form 4n + 3. For example, 17 can be divided only by 17 and by 1. The probability of the existence of another Fermat prime is less than one in a billion. The Nth Prime Page Nth prime through n=10^12, pi(x) through x=3*10^13, Random prime in same range. For a = 2, these are the Mersenne primes, while for a = 10 they are the repunit primes. Prime Number. For example 2, 3, 5, 7…are prime numbers. It seems likely that all further permutable primes are repunits, i.e. Where (p, p+2, p+6) or (p, p+4, p+6) are all prime. ) For explanation of general divisibility rules explained, see Divisibility Rules. Here are the prime numbers in the range 0 to 10,000. Output. {\displaystyle 0\leq 2n\leq p-3} The First 2000 Prime Numbers. 12n+11: 11, 23, 47, 59, 71, 83, 107, 131, 167, 179, 191, 227, 239, 251, 263 (OEIS: A068231), 5, 7, 11, 23, 47, 59, 83, 107, 167, 179, 227, 263, 347, 359, 383, 467, 479, 503, 563, 587, 719, 839, 863, 887, 983, 1019, 1187, 1283, 1307, 1319, 1367, 1439, 1487, 1523, 1619, 1823, 1907 (OEIS: A005385). < − See below).. Want more? Euclid recorded a proof that there is no largest prime number, and many mathematicians and hobbyists continue to search for large prime numbers.. The thousandth prime, prime(1000), is 7919. For example: 2, 3 , 5, 7, 11 are the first five prime numbers. The number which is only divisible by itself and 1 is known as prime number. Primes that having any one of their (base 10) digits changed to any other value will always result in a composite number. Of the form an + d for fixed integers a and d. Also called primes congruent to d modulo a. 10 p 18p − 1 ≡ 1 (mod p2): 5, 7, 37, 331, 33923, 1284043 (OEIS: A244260) Combining the Define Name function and formulas, you can list or generate all of the prime numbers between the two specific numbers. They are also called full reptend primes. 2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 10301, 10501, 10601, 11311, 11411, 12421, 12721, 12821, 13331, 13831, 13931, 14341, 14741 (OEIS: A002385). Determine whether a given whole number in the range 1 to 100 is prime or composite. As of 2018[update], there are 51 known Mersenne primes. 8n+1: 17, 41, 73, 89, 97, 113, 137, 193, 233, 241, 257, 281, 313, 337, 353 (OEIS: A007519) 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, 173, 179, 191, 233, 239, 251, 281, 293, 359, 419, 431, 443, 491, 509, 593, 641, 653, 659, 683, 719, 743, 761, 809, 911, 953 (OEIS: A005384). So 2 is prime (in fact two is the only even prime number!) 5, 11, 17, 29, 37, 41, 53, 59, 67, 71, 97, 101, 127, 149, 179, 191, 223, 227, 251, 257, 269, 307 (OEIS: A028388), 7, 13, 19, 23, 31, 79, 97, 103, 109, 139, 167, 193, 239, 263, 293, 313, 331, 367, 379, 383, 397, 409, 487, 563, 617, 653, 673, 683, 709, 739, 761, 863, 881, 907, 937, 1009, 1033, 1039, 1093 (OEIS: A035497), Primes p for which there are no solutions to Hk ≡ 0 (mod p) and Hk ≡ −ωp (mod p) for 1 ≤ k ≤ p−2, where Hk denotes the k-th harmonic number and ωp denotes the Wolstenholme quotient. 2 x 2 = 4. 10n+9: 19, 29, 59, 79, 89, 109, 139, 149, 179, 199, 229, 239, 269, 349, 359 (OEIS: A030433) 3, 5, 11, 17, 31, 41, 59, 67, 83, 109, 127, 157, 179, 191, 211, 241, 277, 283, 331, 353, 367, 401, 431, 461, 509, 547, 563, 587, 599, 617, 709, 739, 773, 797, 859, 877, 919, 967, 991 (OEIS: A006450). Logic to print prime numbers between 1 to n. Step by step descriptive logic to print all prime numbers between 1 to n. Input upper limit to print prime numbers from user. ± p E More details are in the article for the name. ≤ A prime number has to be a positive integer p is defined as. Recognize that a whole number is a multiple of each of its factors. In other words, 210 can be divided by 1, by itself and at least by 2, 3, 5 and 7. 16843, 2124679 List of factorial primes. Count all prime numbers in a given range whose sum of digits is also prime. There are exactly 26 minimal primes: 2, 3, 5, 7, 11, 19, 41, 61, 89, 409, 449, 499, 881, 991, 6469, 6949, 9001, 9049, 9649, 9949, 60649, 666649, 946669, 60000049, 66000049, 66600049 (OEIS: A071062). Determine whether a given whole number in the range 1 to 100 is a multiple of a given one-digit number. Interface to a list of the first 98 million primes (primes less than 2,000,000,000) Weisstein, Eric W. "Prime Number Sequences". A subset of Mersenne primes of the form 22p−1 − 1 for prime p. 7, 127, 2147483647, 170141183460469231731687303715884105727 (primes in OEIS: A077586), As of June 2017, these are the only known double Mersenne primes, and number theorists think these are probably the only double Mersenne primes. Primes of the form (This, as with its alphabetic counterpart the ambigram, is dependent upon the typeface. 12p − 1 ≡ 1 (mod p2): 2693, 123653 (OEIS: A111027) Prime numbers between 900 and 1000 are: 907 911 919 929 937 941 947 953 967 971 977 983 991 997. Primes p that do not divide the class number of the p-th cyclotomic field. Output. Primes in the Lucas number sequence L0 = 2, L1 = 1, According to the ancient Greek philosopher, 5,040 was the best number that exists, because there are 60 different numbers that it can be divided by. 17p − 1 ≡ 1 (mod p2): 2, 3, 46021, 48947 (OEIS: A128668)[20] 24036583, 25964951, 30402457, 32582657, 37156667, 42643801, 43112609 (OEIS: A000043), As of December 2018[update] four more are known to be in the sequence, but it is not known whether they are the next: Primes p for which p2 divides (p−1)! For Mobile Devices, it is strongly recommended to view this page in "PC mode", or simply view the Divisibility Rules page above. m Primes in the Pell number sequence P0 = 0, P1 = 1, Prime number is a positive integer greater than 1 that is only divisible by 1 and itself. , Here we will see two programs: 1) First program will print the prime numbers between 1 and 100 2) Second program takes the value of n (entered by user) and prints the prime numbers between 1 and n. 7p − 1 ≡ 1 (mod p2): 5, 491531 (OEIS: A123693) The first 1000 prime numbers are given below. ≤ 2, 5, 11, 101, 181, 1181, 1811, 18181, 108881, 110881, 118081, 120121, 10p − 1 ≡ 1 (mod p2): 3, 487, 56598313 (OEIS: A045616) p Chart Prime Numbers. Primes for which there are more prime permutations of some or all the decimal digits than for any smaller number. Below are listed the first prime numbers of many named forms and types. ) {\displaystyle p} Prime Number. − × 21p − 1 ≡ 1 (mod p2): 2 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, 59, 67, 71, 83, 89, 101, 107, 109, 113, 127, 131, 137, 139, 149, 157, 167, 179, 181, 191, 197, 199, 211, 227, 233, 239, 251, 257, 263, 269, 281, 293, 307, 311, 317, 337, 347, 353, 359, 379, 389, 401, 409 (OEIS: A109611). , where the Legendre symbol Of the form Definition. If the sum of a number's digits is a multiple of 3, that number can be divided by 3. 2, 3, 17, 137, 227, 977, 1187, 1493 (OEIS: A042978). 2, 5, 11, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, 101, 107, 113, 131, 137, 149, 167, 173, 179, 191, 197, 227, 233, 239, 251, 257, 263, 269, 281, 293, 311, 317, 347, 353, 359, 383, 389, 401 (OEIS: A003627). A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. is an Euler irregular pair. Here we will see two programs: 1) First program will print the prime numbers between 1 and 100 2) Second program takes the value of n (entered by user) and prints the prime numbers between 1 and n. Of the form k×2n + 1, with odd k and k < 2n. Primes p for which, in a given base b, Chart Prime Numbers. Rahman wants the list of prime numbers available in a range of numbers.Can you help him out? The next term has 6,539 digits. − 37, 59, 67, 101, 103, 131, 149, 157, 233, 257, 263, 271, 283, 293, 307, 311, 347, 353, 379, 389, 401, 409, 421, 433, 461, 463, 467, 491, 523, 541, 547, 557, 577, 587, 593, 607, 613 (OEIS: A000928), Primes p such that (p, p−5) is an irregular pair. x 2, 3, 5, 7, 23, 719, 5039, 39916801, 479001599, 87178291199 These factors can be determined with the help of the prime factorisation method. Lists of prime numbers. ), 11, 101, 181, 619, 16091, 18181, 19861, 61819, 116911, 119611, 160091, 169691, 191161, 196961, 686989, 688889 (sequence A007597 in the OEIS). So, 6 is a 'composite number'. For example, you could create a list containing the first 100 prime numbers, or you would create a list of primes between 1 and 100 (25 primes). Write a program to print all prime numbers in the interval [a,b] (a and b, both inclusive). 15p − 1 ≡ 1 (mod p2): 29131, 119327070011 (OEIS: A242741) Overview of Prime Numbers in Python. Lists of Primes at the Prime Pages. Visit this page to learn how to check whether a number is prime or not. Online prime numbers list. View as a simple list or as a CSV spreadsheet. The fourth Smarandache-Wellin prime is the 355-digit concatenation of the first 128 primes that end with 719. # Prime determination method def Prime_series(number): for iter in range(2,number): if is_prime(iter) == True: print(iter,end = " ") else: pass number = int(input("Enter the input Range : ")) is_prime = lambda number: all( number%i != 0 for i in range(2, int(number**.5)+1) ) Prime_series(number) Output: Explanation: This program determines the range of prime numbers using the lam… 10n+3: 3, 13, 23, 43, 53, 73, 83, 103, 113, 163, 173, 193, 223, 233, 263 (OEIS: A030431) This form is prime for all positive integers n. 2, 11, 1361, 2521008887, 16022236204009818131831320183 (OEIS: A051254). 2, 23, 47, 59, 83, 89, 113, 167, 269, 389, 419, 509, 659, 839, 1049, 1259, 1889 (OEIS: A105440). Three such primes are known; it is not known whether there are more.[13]. 2, 3, 5, 7, 13, 17, 19, 37, 73, 97, 109, 163, 193, 257, 433, 487, 577, 769, 1153, 1297, 1459, 2593, 2917, 3457, 3889, 10369, 12289, 17497, 18433, 39367, 52489, 65537, 139969, 147457 (OEIS: A005109). Primes that remain the same when their decimal digits are read backwards. And the last is a printable list of the first 100 prime numbers to use in a binder or as a Math poster, etc. Prime Numbers. 19, 31, 43, 47, 61, 67, 71, 79, 101, 137, 139, 149, 193, 223, 241, 251, 263, 277, 307, 311, 349, 353, 359, 373, 379, 419, 433, 461, 463, 491, 509, 541, 563, 571, 577, 587 (OEIS: A120337). Most younger students do not need the first hundred prime numbers chart although it is a very handy item for teachers with bright students! A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. 2, 11, 17, 29, 41, 47, 59, 67, 71, 97, 101, 107, 127, 149, 151, 167, 179, 181, 227, 229, 233, 239, 241, 263, 269, 281, 307, 311, 347, 349, 367, 373, 401, 409, 419, 431, 433, 439, 461, 487, 491 (OEIS: A104272). − The classes 10n+d (d = 1, 3, 7, 9) are primes ending in the decimal digit d. 2n+1: 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53 (OEIS: A065091) In other words, 6 can be divided by 1, by itself and at least by 2 and 3. 1 [8], Primes p such that (p, p − 9) is an irregular pair.[8]. :-) Use this prime number chart as an answer key or a practice worksheet. Access to hundreds of pages of award-winning information on prime numbers--with links to thousands of pages elsewhere. Here, we store the interval as lower for lower interval and upper for upper interval, and find prime numbers in that range. So, 210 is a 'composite number'. The list of primes p for which the period length of the decimal expansion of 1/p is unique (no other prime gives the same period). 2, 3, 211, 5, 23, 7, 3331113965338635107, 311, 773, 11, 223, 13, 13367, 1129, 31636373, 17, 233, 19, 3318308475676071413, 37, 211, 23, 331319, 773, 3251, 13367, 227, 29, 547, 31, 241271, 311, 31397, 1129, 71129, 37, 373, 313, 3314192745739, 41, 379, 43, 22815088913, 3411949, 223, 47, 6161791591356884791277 (OEIS: A037274). Primes that are also a prime number when rotated upside down. 13p − 1 ≡ 1 (mod p2): 2, 863, 1747591 (OEIS: A128667)[20] A Prime number can be explained as a finite number that is only divisible by 1 and by itself. Count prime numbers that can be expressed as sum of consecutive prime numbers. 10, Sep 20. − Prime Number List. A different computation found that there are 18,435,599,767,349,200,867,866 primes (roughly 2×1022) below 1024, if the Riemann hypothesis is true.[4]. 8n+7: 7, 23, 31, 47, 71, 79, 103, 127, 151, 167, 191, 199, 223, 239, 263 (OEIS: A007522) The idea to solve this problem is to iterate the val from start to end using a for loop and for every number, if it is greater than 1, check if it divides n. If we find any other number which divides, print that value. Of the form pn# + 1 (a subset of primorial primes). If you want to learn more about Brain, you may want to visit our home page. As of 2018[update], no Wall-Sun-Sun primes are known. A natural number greater than 1 that is not prime is called a composite number.For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself.However, 4 is composite because it is a product (2 × 2) in which both numbers … This include the following: Of the form ⌊θ3n⌋, where θ is Mills' constant. This prime numbers generator is used to generate the list of prime numbers from 1 to a number you specify. Primes that remain prime when read upside down or mirrored in a seven-segment display. (How did you get these? 1 is neither prime nor composite. 2p, 3p, 4p up to N and mark them in the list as not prime numbers. 2, 3, 5, 7, 23, 719, 5039, 39916801, 479001599, 87178291199, 10888869450418352160768000001, 265252859812191058636308479999999, 263130836933693530167218012159999999, 8683317618811886495518194401279999999 (OEIS: A088054), As of August 2019[update] these are the only known Fermat primes, and conjecturally the only Fermat primes. Here, 4 is said to be a composite number. (How did you get these? . A prime number can be divided, without a remainder, only by itself and by 1. prime numbers. [6], a = 2: 3, 5, 17, 257, 65537 (OEIS: A019434). Versão em portugês. 2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 43, 47, 53, 59, 61, 67, 71, 79, 101, 107, 127, 131, 139, 149, 151, 157, 173, 181, 191, 197, 199, 211, 223, 229, 263, 269, 277, 283, 311, 317, 331, 347, 349 (OEIS: A007459). Where p is prime and p+2 is either a prime or semiprime. 3, 7, 31, 211, 2311, 200560490131 (OEIS: A018239[5]). Some facts: The only even prime number is 2. Here, we store the interval as lower for lower interval and upper for upper interval, and find prime numbers in that range. where x = y + 2. Prime Numbers List Full list for prime numbers below 10,000,000,000, partial list for up to 400 digits. The first few prime numbers are {2, 3, 5, 7, 11, ….}. such that 13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, 167, 179, 199, 311, 337, 347, 359, 389, 701, 709, 733, 739, 743, 751, 761, 769, 907, 937, 941, 953, 967, 971, 983, 991 (OEIS: A006567). This prime numbers generator is used to generate first n (up to 1000) prime numbers. What Factors Are 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 113, 131, 197, 199, 311, 337, 373, 719, 733, 919, 971, 991, 1193, 1931, 3119, 3779, 7793, 7937, 9311, 9377, 11939, 19391, 19937, 37199, 39119, 71993, 91193, 93719, 93911, 99371, 193939, 199933, 319993, 331999, 391939, 393919, 919393, 933199, 939193, 939391, 993319, 999331 (OEIS: A068652). (5, 7, 11), (7, 11, 13), (11, 13, 17), (13, 17, 19), (17, 19, 23), (37, 41, 43), (41, 43, 47), (67, 71, 73), (97, 101, 103), (101, 103, 107), (103, 107, 109), (107, 109, 113), (191, 193, 197), (193, 197, 199), (223, 227, 229), (227, 229, 233), (277, 281, 283), (307, 311, 313), (311, 313, 317), (347, 349, 353) (OEIS: A007529, OEIS: A098414, OEIS: A098415). Determine whether a given whole number in the range 1 to 100 is a multiple of a given one-digit number. 2.In the New Name dialog box, in the Name text box, please enter rng … 4 (2,3,4…N). The smallest primer number is 2 . {\displaystyle {{2p-1} \choose {p-1}}\equiv 1{\pmod {p^{4}}}.}. Wikipedia, Prime number and Prime number theorem. As of 2003, these are the only known Wilson primes. Primes that remain prime when the least significant decimal digit is successively removed. A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. This prime numbers generator is used to generate the list of prime numbers from 1 to a number you specify. C Program to find Sum of Prime Numbers from 1 to N. Instead of adding prime numbers from 1 to 100, you can allow the user to decide the minimum and maximum values. Let’s say variable p=2. . 557.935 is an average of first 200 prime numbers mentioned in the below table, by substituting the total sum and count of numbers in the formula. A prime number (or prime integer, often simply called a "prime" for short) is a positive integer that has no positive integer divisors other than 1 and itself. ) Many of the largest known primes are Mersenne primes, numbers that are one less than a power of two.As of December 2020, the eight largest … 4n+3: 3, 7, 11, 19, 23, 31, 43, 47, 59, 67, 71, 79, 83, 103, 107 (OEIS: A002145) Of the form List of Prime Numbers - (up to 251) Example/Guidance. 16p − 1 ≡ 1 (mod p2): 1093, 3511 ( 4p − 1 ≡ 1 (mod p2): 1093, 3511 Definition. 3 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 11311, 11411, 33533, 77377, 77477, 77977, 1114111, 1117111, 3331333, 3337333, 7772777, 7774777, 7778777, 111181111, 111191111, 777767777, 77777677777, 99999199999 (OEIS: A077798). Here is the list of prime numbers up to 100. Prime numbers between 900 and 1000 are: 907 911 919 929 937 941 947 953 967 971 977 983 991 997. To find the first five prime numbers, we start at 2 (remember that 1 is not classed as a prime number). ) Primes p for which there exist n > 0 such that p divides n! The largest known explicit prime (as of Apr 2005) is presented (see Table 1.2), along with Mersenne search-status data. You can also download more prime numbers here As of 2003, these are the only known Wolstenholme primes. {\displaystyle F_{p-\left({\frac {p}{5}}\right)}} 2, 3, 5, 7, 11, 101, 17977, 10619863, 6620830889, 80630964769, 228204732751, 1171432692373, 1398341745571, 10963707205259, 15285151248481, 10657331232548839, 790738119649411319, 18987964267331664557 (OEIS: A049575). 20p − 1 ≡ 1 (mod p2): 281, 46457, 9377747, 122959073 (OEIS: A242982) 13, 109, 193, 433, 769, 1201, 1453, 2029, 3469, 3889, 4801, 10093, 12289, 13873, 18253, 20173, 21169, 22189, 28813, 37633, 43201, 47629, 60493, 63949, 65713, 69313, 73009, 76801, 84673, 106033, 108301, 112909, 115249 (OEIS: A002648), 3, 393050634124102232869567034555427371542904833 (OEIS: A050920). A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself. 12n+7: 7, 19, 31, 43, 67, 79, 103, 127, 139, 151, 163, 199, 211, 223, 271 (OEIS: A068229) Versão em portugês. 3 n Write a program to generate a list of all prime numbers less than 20. [14] This means all digits except the middle digit are equal. 1 {\displaystyle p} Why such page ? Primes p such that ap − 1 ≡ 1 (mod p2) for fixed integer a > 1. In fact, Plato's favourite number was a highly composite number, or an anti-prime. Prime Numbers in the range 100,000 to 200,000, Prime Numbers in the range 200,000 to 300,000, Prime Numbers in the range 300,000 to 400,000, Prime Numbers in the range 400,000 to 500,000, Prime Numbers in the range 500,000 to 600,000, Prime Numbers in the range 600,000 to 700,000, Prime Numbers in the range 700,000 to 800,000, Prime Numbers in the range 800,000 to 900,000, Prime Numbers in the range 900,000 to 1,000,000. ≤ List of all known Mersenne prime numbers along with the discoverer's name, dates of discovery and the method used to prove its primality. The 13th, 14th, and 51st have respectively 157, 183, and 24,862,048 digits. Before starting it is important to note what a prime number is. List of Wilson primes. 294001, 505447, 584141, 604171, 971767, 1062599, 1282529, 1524181, 2017963, 2474431, 2690201, 3085553, 3326489, 4393139 (OEIS: A050249). Fn = Fn−1 + Fn−2. View as a simple list or as a CSV spreadsheet. x 5p − 1 ≡ 1 (mod p2): 2, 20771, 40487, 53471161, 1645333507, 6692367337, 188748146801 (OEIS: A123692) [1], The Goldbach conjecture verification project reports that it has computed all primes below 4×1018. for some ( A circular prime number is a number that remains prime on any cyclic rotation of its digits (in base 10). By Euclid's theorem, there are an infinite number of prime numbers. A prime number … 10n+1: 11, 31, 41, 61, 71, 101, 131, 151, 181, 191, 211, 241, 251, 271, 281 (OEIS: A030430) ≡ A prime number is a number greater than 1 that has exactly two factors.. 1 mod p {\displaystyle {\frac {b^{p-1}-1}{p}}} 3, 11, 37, 101, 9091, 9901, 333667, 909091, 99990001, 999999000001, 9999999900000001, 909090909090909091, 1111111111111111111, 11111111111111111111111, 900900900900990990990991 (OEIS: A040017), 3, 11, 43, 683, 2731, 43691, 174763, 2796203, 715827883, 2932031007403, 768614336404564651, 201487636602438195784363, 845100400152152934331135470251, 56713727820156410577229101238628035243 (OEIS: A000979), 3, 5, 7, 11, 13, 17, 19, 23, 31, 43, 61, 79, 101, 127, 167, 191, 199, 313, 347, 701, 1709, 2617, 3539, 5807, 10501, 10691, 11279, 12391, 14479, 42737, 83339, 95369, 117239, 127031, 138937, 141079, 267017, 269987, 374321 (OEIS: A000978), A prime p > 5, if p2 divides the Fibonacci number F A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself. The number 210 is not a prime number because it is possible to express it as a product of prime factors. MathWorld. 3, 5, 7, 13, 17, 19, 23, 37, 47, 59, 61, 67, 71, 79, 89, 101, 103, 107, 109, 127, 151, 157, 163, 167, 191, 197, 199, 223, 229, 233, 239, 271, 277, 283, 293, 307, 311, 313, 331, 353, 373, 379, 383, 397 (OEIS: A046066). View the Prime Numbers in the range 0 to 10,000 in a neatly formatted table, or download any of the following text files: I generated these prime numbers using the "Sieve of Eratosthenes" algorithm. 25p − 1 ≡ 1 (mod p2): 2, 20771, 40487, 53471161, 1645333507, 6692367337, 188748146801. ' constant to 100 seems likely that all further permutable primes are known also download prime... 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