The Exploring Primeness Project

 

Neil Fernandez

Some sequences noted in connection with the order of primeness, F(p)

 

 

This document gives further terms of sequences mentioned in the discussion of the order of primeness F(p).

 

 

Primes p with F(p)=1 (first 200)

2, 7, 13, 19, 23, 29, 37, 43, 47, 53, 61, 71, 73, 79, 89, 97, 101, 103, 107, 113, 131, 137, 139, 149, 151, 163, 167, 173, 181, 193, 197, 199, 223, 227, 229, 233, 239, 251, 257, 263, 269, 271, 281, 293, 307, 311, 313, 317, 337, 347, 349, 359, 373, 379, 383, 389, 397, 409, 419, 421, 433, 439, 443, 449, 457, 463, 467, 479, 487, 491, 499, 503, 521, 523, 541, 557, 569, 571, 577, 593, 601, 607, 613, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 719, 727, 733, 743, 751, 757, 761, 769, 787, 809, 811, 821, 823, 827, 829, 839, 853, 857, 863, 881, 883, 887, 907, 911, 929, 937, 941, 947, 953, 971, 977, 983, 997, 1009, 1013, 1019, 1021, 1033, 1039, 1049, 1051, 1061, 1069, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1163, 1181, 1187, 1193, 1213, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1423, 1427, 1429, 1439, 1451, 1453, 1459, 1481, 1483, 1487, 1489, 1493, 1511, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1601, 1607, 1609, ...

 

Primes p with F(p)=2 (first 100)

3, 17, 41, 67, 83, 109, 157, 191, 211, 241, 283, 353, 367, 401, 461, 509, 547, 563, 587, 617, 739, 773, 797, 859, 877, 967, 991, 1031, 1087, 1171, 1201, 1217, 1409, 1433, 1447, 1471, 1499, 1597, 1621, 1669, 1723, 1741, 1823, 1913, 2027, 2063, 2081, 2099, 2269, 2341, 2351, 2417, 2549, 2609, 2647, 2683, 2719, 2803, 2897, 2909, 3019, 3067, 3109, 3169, 3229, 3299, 3319, 3407, 3469, 3517, 3559, 3593, 3733, 3761, 3911, 4027, 4133, 4153, 4217, 4339, 4421, 4463, 4517, 4567, 4663, 4759, 4787, 4801, 4877, 4933, 4943, 5021, 5059, 5107, 5189, 5281, 5441, 5503, 5557, 5651, ...

 

Primes p with F(p)=3 (first 100)

5, 59, 179, 331, 431, 599, 919, 1153, 1297, 1523, 1847, 2381, 2477, 2749, 3259, 3637, 3943, 4091, 4273, 4549, 5623, 5869, 6113, 6661, 6823, 7607, 7841, 8221, 8719, 9461, 9739, 9859, 11743, 11953, 12097, 12301, 12547, 13469, 13709, 14177, 14723, 14867, 15641, 16519, 17627, 17987, 18149, 18311, 20063, 20773, 20899, 21529, 22811, 23431, 23801, 24107, 24509, 25423, 26371, 26489, 27689, 28109, 28573, 29153, 29803, 30557, 30781, 31667, 32341, 32797, 33203, 33569, 35023, 35311, 36887, 38153, 39239, 39451, 40151, 41491, 42293, 42697, 43283, 43889, 44879, 45971, 46279, 46451, 47297, 47857, 47963, 48821, 49207, 49739, 50591, 51599, 53353, 54013, 54601, 55681, ...

 

Primes p with F(p)=4 (first 32, less than 104729)

11, 277, 1063, 2221, 3001, 4397, 7193, 9319, 10631, 12763, 15823, 21179, 22093, 24859, 30133, 33967, 37217, 38833, 40819, 43651, 55351, 57943, 60647, 66851, 68639, 77431, 80071, 84347, 90023, 98519, 101701, 103069, ...

 

Primes p with F(p)=5 (first 8, less than 104729)

31, 1787, 8527, 19577, 27457, 42043, 72727, 96797, ...

 

Primes p with F(p)=6 (first 3, less than 104729)

127, 15299, 87803, ...

 

Primes p with F(p)=7, 8, 9

The only prime <104729 with F(p)=7 is 709

The only prime <104729 with F(p)=8 is 5381

The only prime <104729 with F(p)=9 is 52711

 

Note that 104729 is p(10000), the 10,000th prime.

 

Primes p with F(p)>1 (first 100)

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, 1031, 1063, 1087, 1153, 1171, 1201, 1217, 1297, 1409, 1433, 1447, 1471, 1499, 1523, 1597, 1621, 1669, 1723, 1741, 1787, 1823, 1847, 1913, 2027, 2063, 2081, 2099, 2221, 2269, 2341, 2351, 2381, 2417, 2477, 2549, 2609, 2647, 2683, 2719, 2749, 2803, 2897, 2909, 3001, 3019, 3067, 3109, 3169, 3229, 3259, 3299, 3319, 3407, 3469, 3517, 3559, 3593, 3637, 3733, 3761, 3911, ...

 

Primes p with F(p)>2 (first 100)

5, 11, 31, 59, 127, 179, 277, 331, 431, 599, 709, 919, 1063, 1153, 1297, 1523, 1787, 1847, 2221, 2381, 2477, 2749, 3001, 3259, 3637, 3943, 4091, 4273, 4397, 4549, 5381, 5623, 5869, 6113, 6661, 6823, 7193, 7607, 7841, 8221, 8527, 8719, 9319, 9461, 9739, 9859, 10631, 11743, 11953, 12097, 12301, 12547, 12763, 13469, 13709, 14177, 14723, 14867, 15299, 15641, 15823, 16519, 17627, 17987, 18149, 18311, 19577, 20063, 20773, 20899, 21179, 21529, 22093, 22811, 23431, 23801, 24107, 24509, 24859, 25423, 26371, 26489, 27457, 27689, 28109, 28573, 29153, 29803, 30133, 30557, 30781, 31667, 32341, 32797, 33203, 33569, 33967, 35023, 35311, 36887, ...

 

Primes p with F(p)>3 (first 46, less than 104729)

11, 31, 127, 277, 709, 1063, 1787, 2221, 3001, 4397, 5381, 7193, 8527, 9319, 10631, 12763, 15299, 15823, 19577, 21179, 22093, 24859, 27457, 30133, 33967, 37217, 38833, 40819, 42043, 43651, 52711, 55351, 57943, 60647, 66851, 68639, 72727, 77431, 80071, 84347, 87803, 90023, 96797, 98519, 101701, 103069, ...

 

 

Smallest primes for which F(p)=n (first 9, less than 104729)

2, 3, 5, 11, 31, 127, 709, 5381, 52711, ...

 

F(p(n)) for successive primes p(n) (first 500)

1, 2, 3, 1, 4, 1, 2, 1, 1, 1, 5, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 6, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 5, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, ...

 

 

Copyright Neil Fernandez 1999

Last modified 8 August 1999