يوجد عدد لانهائي من عدد أولي الأعداد الأولية يمكن حتى تتولد بعديد من المعادلات معادلات الأعداد الأولية.أول 500 عدد في القائمة السفلى, تتبعها قوائم لأول أعداد أولية من أنواع مختلفة مرتبة ترتيبا أبجديا .

أول 500 من الأعداد الأولية

يوجد 20 عدد أولي متتالي في جميع من ال 25 صف .

(sequence A000040 in OEIS).

The Goldbach conjecture verification project reports that it has computed all primes below 10¹⁸. That means 24,739,954,287,740,860 primes, but they were not stored. There are known formulas to evaluate the prime-counting function (the number of primes below a given value) faster than computing the primes. This has been used to compute that there are 1,925,320,391,606,803,968,923 primes below 10²³.

قائمة الأعداد الأولية حسب النوع

أدناه قائمة بأول أعداد أولية من أسماء مختلفة, أنواع مختلفة . لمزيد من التفاصيل أنظر الموضوعة الإسم. n هو رقم طبيعي (يضم الصفر) في التعريفات.

عدد أولي فريد

لا تستغرب أنّ هذا العدد الضخم -الذي سنعلّمك كيف من الممكن أن يُقرأ- هوعدد أولي

357686312646216567629137

يُقرأ بالشكل

357 سكستليون و686 كوينتليون و312 كوادريليون و646 تريليون و216 بليون و567 مليون و629 ألف و137

يتميّز هذا العدد الأولي المؤلّف من 24 منزلة بأنّه كلّما أُزيلت مرتبة من اليسار سينتج عدد أولي جديد، أي العدد:

57686312646216567629137

أيضًا عدد أولي، وكذلك العدد:

7686312646216567629137

أيضًا عدد أولي، وكذلك العدد:

686312646216567629137

أيضًا عدد أولي، وكذلك العدد:

86312646216567629137

إلى غير ذلك… حتى نصل إلى: 137، 13، 7

ينتمي هذا العدد إلى مجموعة تُدعى left-truncatable primes أي الأعـداد الأولية التي تُنتِج أعدادًا أوّليّة جديدة كلّما اقتُطع منها منزلة من اليسار، والتي تحوي 4260 عددًا، وصاحبنا هذا هوأكبرها حتّى الآن.

الأعداد الأولية المتوازنة

الأعداد الأولية التى هى المتوسط للأعداد الأولية السابقة والأعداد الأولية الآتية .

5, 53, 157, 173, 211, 257, 263, 373, 563, 593, 607, 653, 733, 947, 977, 1103, 1123, 1187, 1223, 1367, 1511, 1747, 1753, 1907, 2287, 2417, 2677, 2903, 2963, 3307, 3313, 3637, 3733, 4013, 4409, 4457, 4597, 4657, 4691, 4993, 5107, 5113, 5303, 5387, 5393 (نطقب:OEIS2C)

رقم بل أرقام أولية

الأعداد الأولية التى هى جزء من مجموعة جزء من مجموعة حيث n أعضاء.

2, 5, 877, 27644437, 35742549198872617291353508656626642567, 359334085968622831041960188598043661065388726959079837. The next term has 6539 digits. (نطقب:OEIS2C)

Carol primes

Of the form ${\displaystyle (2^{n -1)^{2 -2$.

7, 47, 223, 3967, 16127, 1046527, 16769023, 1073676287, 68718952447, 274876858367, 4398042316799, 1125899839733759, 18014398241046527, 1298074214633706835075030044377087 (نطقب:OEIS2C)

Centered decagonal primes

Of the form ${\displaystyle 5(n^{2 -n)+1$.

11, 31, 61, 101, 151, 211, 281, 661, 911, 1051, 1201, 1361, 1531, 1901, 2311, 2531, 3001, 3251, 3511, 4651, 5281, 6301, 6661, 7411, 9461, 9901, 12251, 13781, 14851, 15401, 18301, 18911, 19531, 20161, 22111, 24151, 24851, 25561, 27011, 27751 (نطقب:OEIS2C)

Centered heptagonal primes

Of the form (7n² − 7n + 2) / 2.

43, 71, 197, 463, 547, 953, 1471, 1933, 2647, 2843, 3697, 4663, 5741, 8233, 9283, 10781, 11173, 12391, 14561, 18397, 20483, 29303, 29947, 34651, 37493, 41203, 46691, 50821, 54251, 56897, 57793, 65213, 68111, 72073, 76147, 84631, 89041, 93563 (primes in نطقب:OEIS2C)

Centered square primes

Of the form ${\displaystyle n^{2 +(n+1)^{2$.

5, 13, 41, 61, 113, 181, 313, 421, 613, 761, 1013, 1201, 1301, 1741, 1861, 2113, 2381, 2521, 3121, 3613, 4513, 5101, 7321, 8581, 9661, 9941, 10513, 12641, 13613, 14281, 14621, 15313, 16381, 19013, 19801, 20201, 21013, 21841, 23981, 24421, 26681 (نطقب:OEIS2C)

Centered triangular primes

Of the form (3n² + 3n + 2) / 2.

19, 31, 109, 199, 409, 571, 631, 829, 1489, 1999, 2341, 2971, 3529, 4621, 4789, 7039, 7669, 8779, 9721, 10459, 10711, 13681, 14851, 16069, 16381, 17659, 20011, 20359, 23251, 25939, 27541, 29191, 29611, 31321, 34429, 36739, 40099, 40591, 42589 (نطقب:OEIS2C)

Chen primes

p is prime and p + 2 is either a prime or semiprime.

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 (نطقب:OEIS2C)

Cousin primes

(p, p + 4) are both prime.

(3, 7), (7, 11), (13, 17), (19, 23), (37, 41), (43, 47), (67, 71), (79, 83), (97, 101), (103, 107), (109, 113), (127, 131), (163, 167), (193, 197), (223, 227), (229, 233), (277, 281) (نطقب:OEIS2C, نطقب:OEIS2C)

Cuban primes

Of the form ${\displaystyle {\tfrac {x^{3 -y^{3 {x-y$, ${\displaystyle x=y+1$:

7, 19, 37, 61, 127, 271, 331, 397, 547, 631, 919, 1657, 1801, 1951, 2269, 2437, 2791, 3169, 3571, 4219, 4447, 5167, 5419, 6211, 7057, 7351, 8269, 9241, 10267, 11719, 12097, 13267, 13669, 16651, 19441, 19927, 22447, 23497, 24571, 25117, 26227, 27361, 33391, 35317 (نطقب:OEIS2C)

Of the form ${\displaystyle {\tfrac {x^{3 -y^{3 {x-y$, ${\displaystyle x=y+2$:

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 (نطقب:OEIS2C)

Cullen primes

Of the form n · 2ⁿ + 1.

3, 393050634124102232869567034555427371542904833 (نطقب:OEIS2C)

Dihedral primes

Primes that remain prime when read upside down or mirrored in a seven-segment display.

2, 5, 11, 101, 181, 1181, 1811, 18181, 108881, 110881, 118081, 120121, 121021, 121151, 150151, 151051, 151121, 180181, 180811, 181081 (نطقب:OEIS2C)

أعداد مرسن الأولية المزدوجة

Of the form ${\displaystyle 2^{(2^{p -1) -1$ for prime p.

7, 127, 2147483647, 170141183460469231731687303715884105727 (primes in نطقب:OEIS2C)

As of January 2008, these are the only known double Mersenne primes (subset of Mersenne primes.)

Eisenstein primes without imaginary part

Eisenstein integers that are irreducible and real numbers (primes of form 3n − 1).

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 (نطقب:OEIS2C)

Emirps

Primes which become a different prime when their decimal digits are reversed.

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 (نطقب:OEIS2C)

Euclid primes

Of the form p_n# + 1 (a subset of primorial primes).

3, 7, 31, 211, 2311, 200560490131 (نطقب:OEIS2C)

Even prime

Of the form 2n.

2

The only even prime is 2. 2 is therefore sometimes called "the oddest prime" as a pun on the non-mathematical meaning of "odd".[1]

Factorial primes

Of the form n! − 1 or n! + 1.

2, 3, 5, 7, 23, 719, 5039, 39916801, 479001599, 87178291199, 10888869450418352160768000001, 265252859812191058636308479999999, 263130836933693530167218012159999999, 8683317618811886495518194401279999999 (نطقب:OEIS2C)

Fermat primes

Of the form ${\displaystyle 2^{2^{n +1$.

3, 5, 17, 257, 65537 (نطقب:OEIS2C)

As of January 2008, these are the only known Fermat primes.

Fibonacci primes

Primes in the Fibonacci sequence F₀ = 0, F₁ = 1, F_n = F_n-1 + F_n-2.

2, 3, 5, 13, 89, 233, 1597, 28657, 514229, 433494437, 2971215073, 99194853094755497, 1066340417491710595814572169, 19134702400093278081449423917 (نطقب:OEIS2C)

Fortunate primes

Fortunate numbers that are prime (it has been conjectured they all are).

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 (نطقب:OEIS2C)

Gaussian primes

Prime elements of the Gaussian integers (primes of form 4n + 3).

3, 7, 11, 19, 23, 31, 43, 47, 59, 67, 71, 79, 83, 103, 107, 127, 131, 139, 151, 163, 167, 179, 191, 199, 211, 223, 227, 239, 251, 263, 271, 283, 307, 311, 331, 347, 359, 367, 379, 383, 419, 431, 439, 443, 463, 467, 479, 487, 491, 499, 503 (نطقب:OEIS2C)

Genocchi number primes

17

The only prime Genocchi number is 17 (and -3 if negative primes are included).

Good primes

Primes p_n for which p_n² > p_i−1 × p_i+1 for all 1 ≤ i ≤ n−1, where p_n is the nth prime.

5, 11, 17, 29, 37, 41, 53, 59, 67, 71, 97, 101, 127, 149, 179, 191, 223, 227, 251, 257, 269, 307 (نطقب:OEIS2C)

Happy primes

Happy numbers that are prime.

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 (نطقب:OEIS2C)

Higgs primes for squares

Primes p for which p − 1 divides the square of the product of all earlier terms.

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 (نطقب:OEIS2C)

Highly cototient number primes

Primes that are a cototient more often than any integer below it except 1.

2, 23, 47, 59, 83, 89, 113, 167, 269, 389, 419, 509, 659, 839, 1049, 1259, 1889 (نطقب:OEIS2C)

Irregular primes

Odd primes p which divide the class number of the p-th cyclotomic field.

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, 617, 619 (نطقب:OEIS2C)

Kynea primes

Of the form ${\displaystyle (2^{n +1)^{2 -2$.

7, 23, 79, 1087, 66047, 263167, 16785407, 1073807359, 17180131327, 68720001023, 4398050705407, 70368760954879, 18014398777917439, 18446744082299486207 (نطقب:OEIS2C)

Left-truncatable primes

Primes that remain prime when the leading decimal digit is successively removed.

2, 3, 5, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 97, 113, 137, 167, 173, 197, 223, 283, 313, 317, 337, 347, 353, 367, 373, 383, 397, 443, 467, 523, 547, 613, 617, 643, 647, 653, 673, 683 (نطقب:OEIS2C)

Leyland primes

Of the form x^y + y^x with 1 < x ≤ y.

17, 593, 32993, 2097593, 8589935681, 59604644783353249, 523347633027360537213687137, 43143988327398957279342419750374600193 (نطقب:OEIS2C)

Long primes

Primes p for which, in a given base b, ${\displaystyle \frac{b^{p-<!--\; -\; -->1}-<!--\; -\; -->1}{p}}$p for base 10:

7, 17, 19, 23, 29, 47, 59, 61, 97, 109, 113, 131, 149, 167, 179, 181, 193, 223, 229, 233, 257, 263, 269, 313, 337, 367, 379, 383, 389, 419, 433, 461, 487, 491, 499, 503, 509, 541, 571, 577, 593 (نطقب:OEIS2C)

Lucas primes

Primes in the Lucas number sequence L₀ = 2, L₁ = 1, L_n = L_n-1 + L_n-2.

2, 3, 7, 11, 29, 47, 199, 521, 2207, 3571, 9349, 3010349, 54018521, 370248451, 6643838879, 119218851371, 5600748293801, 688846502588399, 32361122672259149 (نطقب:OEIS2C)

Lucky primes

Lucky numbers that are prime.

3, 7, 13, 31, 37, 43, 67, 73, 79, 127, 151, 163, 193, 211, 223, 241, 283, 307, 331, 349, 367, 409, 421, 433, 463, 487, 541, 577, 601, 613, 619, 631, 643, 673, 727, 739, 769, 787, 823, 883, 937, 991, 997 (نطقب:OEIS2C)

Markov primes

Primes p for which there exist integers x and y such that ${\displaystyle x^{2 +y^{2 +p^{2 =3xyp$.

2, 5, 13, 29, 89, 233, 433, 1597, 2897, 5741, 7561, 28657, 33461, 43261, 96557, 426389, 514229 (primes in نطقب:OEIS2C)

أعداد مرسن الأولية

Of the form 2ⁿ − 1. The first 12:

3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, 162259276829213363391578010288127, 170141183460469231731687303715884105727 (نطقب:OEIS2C)

As of September 2008, there are 46 known Mersenne primes. The 13th, 14th, and 46th (based upon size), respectively, have 157, 183, and 12,978,189 digits.

Mills primes

Of the form ${\displaystyle \lfloor \theta ^{3^{n \;\rfloor$, where θ is Mills' constant. This form is prime for all positive integers n.

2, 11, 1361, 2521008887, 16022236204009818131831320183 (نطقب:OEIS2C)

Minimal primes

Primes for which there is no shorter sub-sequence of the decimal digits that form a 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 (نطقب:OEIS2C)

Motzkin primes

Primes that are the number of different ways of drawing non-intersecting chords on a circle between n points.

2, 127, 15511, 953467954114363 (نطقب:OEIS2C)

Newman-Shanks-Williams primes

Newman-Shanks-Williams numbers that are prime.

7, 41, 239, 9369319, 63018038201, 489133282872437279, 19175002942688032928599 (نطقب:OEIS2C)

Odd primes

Of the form 2n - 1.

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 (نطقب:OEIS2C)

All prime numbers except the prime 2 are odd.

Padovan primes

Primes in the Padovan sequence ${\displaystyle P(0)=P(1)=P(2)=1$, ${\displaystyle P(n)=P(n-2)+P(n-3)$.

2, 3, 5, 7, 37, 151, 3329, 23833, 13091204281, 3093215881333057, 1363005552434666078217421284621279933627102780881053358473 (نطقب:OEIS2C)

Palindromic primes

Primes that remain the same when their decimal digits are read backwards.

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 (نطقب:OEIS2C)

Pell primes

Primes in the Pell number sequence P₀ = 0, P₁ = 1, P_n = 2P_n-1 + P_n-2.

2, 5, 29, 5741, 33461, 44560482149, 1746860020068409, 68480406462161287469, 13558774610046711780701, 4125636888562548868221559797461449 (نطقب:OEIS2C)

Permutable primes

Any permutation of the decimal digits is a prime.

2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 113, 131, 199, 311, 337, 373, 733, 919, 991, 1111111111111111111, 11111111111111111111111 (نطقب:OEIS2C)

It seems likely that all further permutable primes are repunits, i.e. contain only the digit 1.

Perrin primes

Primes in the Perrin number sequence P(0) = 3, P(1) = 0, P(2) = 2, P(n) = P(n − 2) + P(n − 3).

2, 3, 5, 7, 17, 29, 277, 367, 853, 14197, 43721, 1442968193, 792606555396977, 187278659180417234321, 66241160488780141071579864797 (نطقب:OEIS2C)

Pierpont primes

Of the form ${\displaystyle 2^u{3}^v+1}$u,v ≥ 0.

These are also class 1- primes.

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 (نطقب:OEIS2C)

Pillai primes

Primes p for which there exist n > 0 such that p divides n! + 1 and n does not divide p − 1.

23, 29, 59, 61, 67, 71, 79, 83, 109, 137, 139, 149, 193, 227, 233, 239, 251, 257, 269, 271, 277, 293, 307, 311, 317, 359, 379, 383, 389, 397, 401, 419, 431, 449, 461, 463, 467, 479, 499 (نطقب:OEIS2C)

Primeval primes

Primes for which there are more prime permutations of some or all the decimal digits than for any smaller number.

2, 13, 37, 107, 113, 137, 1013, 1237, 1367, 10079 (نطقب:OEIS2C)

Primorial primes

Of the form p_n# − 1 or p_n# + 1.

3, 5, 7, 29, 31, 211, 2309, 2311, 30029, 200560490131, 304250263527209, 23768741896345550770650537601358309 (union of نطقب:OEIS2C and نطقب:OEIS2C)

Proth primes

Of the form k · 2ⁿ + 1 with odd k and k < 2ⁿ.

3, 5, 13, 17, 41, 97, 113, 193, 241, 257, 353, 449, 577, 641, 673, 769, 929, 1153, 1217, 1409, 1601, 2113, 2689, 2753, 3137, 3329, 3457, 4481, 4993, 6529, 7297, 7681, 7937, 9473, 9601, 9857 (نطقب:OEIS2C)

Pythagorean primes

Of the form 4n + 1.

5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137, 149, 157, 173, 181, 193, 197, 229, 233, 241, 257, 269, 277, 281, 293, 313, 317, 337, 349, 353, 373, 389, 397, 401, 409, 421, 433, 449 (نطقب:OEIS2C)

Prime quadruplets

(p, p+2, p+6, p+8) are all prime.

(5, 7, 11, 13), (11, 13, 17, 19), (101, 103, 107, 109), (191, 193, 197, 199), (821, 823, 827, 829), (1481, 1483, 1487, 1489), (1871, 1873, 1877, 1879), (2081, 2083, 2087, 2089), (3251, 3253, 3257, 3259), (3461, 3463, 3467, 3469), (5651, 5653, 5657, 5659), (9431, 9433, 9437, 9439) (نطقب:OEIS2C, نطقب:OEIS2C, نطقب:OEIS2C, نطقب:OEIS2C)

Ramanujan primes

Integers R_n that are the smallest to give at least n primes from x/2 to x for all x ≥ R_n (all such integers are primes).

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 (نطقب:OEIS2C)

Regular primes

Primes p which do not divide the class number of the p-th cyclotomic field.

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 43, 47, 53, 61, 71, 73, 79, 83, 89, 97, 107, 109, 113, 127, 137, 139, 151, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 239, 241, 251, 269, 277, 281 (نطقب:OEIS2C)

Repunit primes

Primes containing only the decimal digit 1.

11, 1111111111111111111, 11111111111111111111111 (نطقب:OEIS2C)

The next have 317 and 1031 digits.

Primes in residue classes

Of form a · n + d for fixed a and d. Also called primes congruent to d modulo a.

Three cases have their own entry: 2n+1 are the odd primes, 4n+1 are Pythagorean primes, 4n+3 are the integer Gaussian primes.

2n+1: 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53 (نطقب:OEIS2C)
4n+1: 5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137 (نطقب:OEIS2C)
4n+3: 3, 7, 11, 19, 23, 31, 43, 47, 59, 67, 71, 79, 83, 103, 107 (نطقب:OEIS2C)
6n+1: 7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 97, 103, 109, 127, 139 (نطقب:OEIS2C)
6n+5: 5, 11, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, 101, 107, 113 (نطقب:OEIS2C)
8n+1: 17, 41, 73, 89, 97, 113, 137, 193, 233, 241, 257, 281, 313, 337, 353 (نطقب:OEIS2C)
8n+3: 3, 11, 19, 43, 59, 67, 83, 107, 131, 139, 163, 179, 211, 227, 251 (نطقب:OEIS2C)
8n+5: 5, 13, 29, 37, 53, 61, 101, 109, 149, 157, 173, 181, 197, 229, 269 (نطقب:OEIS2C)
8n+7: 7, 23, 31, 47, 71, 79, 103, 127, 151, 167, 191, 199, 223, 239, 263 (نطقب:OEIS2C)
10n+1: 11, 31, 41, 61, 71, 101, 131, 151, 181, 191, 211, 241, 251, 271, 281 (نطقب:OEIS2C)
10n+3: 3, 13, 23, 43, 53, 73, 83, 103, 113, 163, 173, 193, 223, 233, 263 (نطقب:OEIS2C)
10n+7: 7, 17, 37, 47, 67, 97, 107, 127, 137, 157, 167, 197, 227, 257, 277 (نطقب:OEIS2C)
10n+9: 19, 29, 59, 79, 89, 109, 139, 149, 179, 199, 229, 239, 269, 349, 359 (نطقب:OEIS2C)
...

10n+d (d = 1, 3, 7, 9) are primes ending in the decimal digit d.

Right-truncatable primes

Primes that remain prime when the last decimal digit is successively removed.

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 (نطقب:OEIS2C)

Safe primes

p and (p-1) / 2 are both prime.

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 (نطقب:OEIS2C)

Self primes in base 10

Primes that cannot be generated by any integer added to the sum of its decimal digits.

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 (نطقب:OEIS2C)

Sexy primes

(p, p + 6) are both prime.

(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) (نطقب:OEIS2C, نطقب:OEIS2C)

Smarandache-Wellin primes

Primes which are the concatenation of the first n primes written in decimal.

2, 23, 2357 (نطقب:OEIS2C)

The fourth Smarandache-Wellin prime is the concatenation of the first 128 primes which end with 719.

Sophie Germain primes

p and 2p + 1 are both prime.

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 (نطقب:OEIS2C)

Star primes

Of the form 6n(n - 1) + 1.

13, 37, 73, 181, 337, 433, 541, 661, 937, 1093, 2053, 2281, 2521, 3037, 3313, 5581, 5953, 6337, 6733, 7561, 7993, 8893, 10333, 10837, 11353, 12421, 12973, 13537, 15913, 18481 (نطقب:OEIS2C)

Stern primes

Primes that are not the sum of a smaller prime and twice the square of a nonzero integer.

2, 3, 17, 137, 227, 977, 1187, 1493 (نطقب:OEIS2C)

As of January 2008, these are the only known Stern primes, and possibly the only existing.

Super-primes

Primes with a prime index in the sequence of prime numbers (the 2nd, 3rd, 5th, ... prime).

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 (نطقب:OEIS2C)

Supersingular primes

There are exactly fifteen supersingular primes:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71 (نطقب:OEIS2C)

Thabit number primes

Of the form ثلاثة · 2ⁿ - 1.

2, 5, 11, 23, 47, 191, 383, 6143, 786431, 51539607551, 824633720831, 26388279066623, 108086391056891903, 55340232221128654847, 226673591177742970257407 (نطقب:OEIS2C)

Prime triplets

(p, p+2, p+6) or (p, p+4, p+6) are all prime.

(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) (نطقب:OEIS2C, نطقب:OEIS2C, نطقب:OEIS2C)

Twin primes

(p, p + 2) are both prime.

(3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73), (101, 103), (107, 109), (137, 139), (149, 151), (179, 181), (191, 193), (197, 199), (227, 229), (239, 241), (269, 271), (281, 283), (311, 313), (347, 349), (419, 421), (431, 433), (461, 463) (نطقب:OEIS2C, نطقب:OEIS2C)

Ulam number primes

Ulam numbers that are prime.

2, 3, 11, 13, 47, 53, 97, 131, 197, 241, 409, 431, 607, 673, 739, 751, 983, 991, 1103, 1433, 1489, 1531, 1553, 1709, 1721, 2371, 2393, 2447, 2633, 2789, 2833, 2897 (نطقب:OEIS2C)

Unique primes

Primes p for which the period length of 1/p is unique (no other prime gives the same).

3, 11, 37, 101, 9091, 9901, 333667, 909091, 99990001, 999999000001, 9999999900000001, 909090909090909091, 1111111111111111111, 11111111111111111111111, 900900900900990990990991 (نطقب:OEIS2C)

Wagstaff primes

Of the form (2ⁿ + 1) / 3.

3, 11, 43, 683, 2731, 43691, 174763, 2796203, 715827883, 2932031007403, 768614336404564651, 201487636602438195784363, 845100400152152934331135470251, 56713727820156410577229101238628035243 (نطقب:OEIS2C)

n values:

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 (نطقب:OEIS2C)

Wedderburn-Etherington number primes

Wedderburn-Etherington numbers that are prime.

2, 3, 11, 23, 983, 2179, 24631, 3626149, 253450711, 596572387 (primes in نطقب:OEIS2C)

Wieferich primes

Primes p for which p² divides 2^{p − 1} − 1

1093, 3511 (نطقب:OEIS2C)

As of January 2008, these are the only known Wieferich primes.

Wilson primes

Primes p for which p² divides (p − 1)! + 10

5, 13, 563 (نطقب:OEIS2C)

As of January 2008, these are the only known Wilson primes.

Wolstenholme primes

Primes p for which the binomial coefficient ${\displaystyle {{2p-1 \choose {p-1 \equiv 1{\pmod {p^{4$.

16843, 2124679 (نطقب:OEIS2C)

As of January 2008, these are the only known Wolstenholme primes.

Woodall primes

Of the form n · 2ⁿ − 1.

7, 23, 383, 32212254719, 2833419889721787128217599, 019786453345410, 477691310985204141824805662288248831 (نطقب:OEIS2C)

انظر أيضاً

• Largest known prime
• List of numbers
• Probable prime
• Pseudoprime
• Strobogrammatic prime
• Strong prime
• Wall-Sun-Sun prime
• Wieferich pair

Notes

وصلات خارجية

• https://elmahatta.com/%D8%A3%D9%83%D8%A8%D8%B1-%D8%B9%D8%AF%D8%AF-%D8%A3%D9%88%D9%84%D9%8A-%D8%A7%D9%84%D8%A3%D8%B9%D8%AF%D8%A7%D8%AF-%D8%A7%D9%84%D8%A3%D9%88%D9%84%D9%8A%D8%A9/
• Lists of Primes at the Prime Pages.
• Interface to a list of the first 98 million primes (primes less than 2,000,000,000)
• Eric W. Weisstein, Prime Number Sequences at MathWorld.
• Selected prime related sequences in OEIS.