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Pierpont primes
A prime  $p$  is a Pierpont prime if it can be written as  $p = 1+2^u\cdot3^v$, for  $u,v\ge0$.

A.M.Gleason has proved that a regular polygon of  $n$  sides can be constructed by ruler, compass and angle-trisector if and only if  $n = 2^r\cdot3^s\cdot p_1\cdot p_2\cdots p_k$, where the  $p_i$'s are distinct Pierpont primes.

Compare with the polygons constructible with ruler and compass only.

The first Pierpont primes are 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, 209953 more terms

Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here
remainders of Pierpont primes
Useful links Wikipedia, Pierpont prime
Mathworld, Pierpont Prime
OEIS, Sequence A005109
Pierpont primes can also be... (you may click on names or numbers and on + to get more values)

a-pointer 13 1153 aban 13 17 19 37 73 97 109 163 193 257 433 487 577 769 alt.fact. 19 alternating 109 163 769 10369 amenable 13 17 37 73 97 109 193 257 433 577 + 120932353 169869313 483729409 725594113 apocalyptic 2593 3889 10369 12289 17497 18433 arithmetic 13 17 19 37 73 97 109 163 193 257 + 2654209 5038849 5308417 8503057 balanced p. 257 18433 c.square 13 c.triangular 19 109 canyon 109 769 10369 52489 Chen 13 17 19 37 109 257 487 577 769 1297 + 629857 995329 5308417 57395629 congruent 13 37 109 257 487 2917 39367 331777 839809 5308417 constructible 17 257 65537 Cunningham 17 37 257 577 1297 2917 65537 147457 331777 746497 + 6347497291777 14281868906497 39582418599937 142657607172097 cyclic 13 17 19 37 73 97 109 163 193 257 + 2654209 5038849 5308417 8503057 d-powerful 3457 de Polignac 629857 746497 1492993 86093443 deficient 13 17 19 37 73 97 109 163 193 257 + 2654209 5038849 5308417 8503057 dig.balanced 19 37 163 economical 13 17 19 37 73 97 109 163 193 257 + 8503057 11337409 14155777 19131877 emirp 13 17 37 73 97 769 1153 3889 12289 995329 1179649 120932353 equidigital 13 17 19 37 73 97 109 163 193 257 + 8503057 11337409 14155777 19131877 evil 17 163 257 1297 2593 10369 17497 65537 139969 331777 + 120932353 169869313 483729409 725594113 fibodiv 19 Fibonacci 13 Friedman 139969 147457 209953 472393 629857 786433 good prime 17 37 97 257 3457 65537 happy 13 19 97 109 193 487 52489 hex 19 37 Hogben 13 73 hungry 17 iban 17 73 iccanobiF 13 idoneal 13 37 inconsummate 65537 junction 109 2917 786433 katadrome 73 97 Leyland 17 lucky 13 37 73 163 193 433 487 577 769 1459 + 39367 147457 209953 5038849 metadrome 13 17 19 37 257 1459 3457 modest 13 19 109 433 mountain 163 193 487 1297 2593 nialpdrome 73 97 433 oban 13 17 19 37 73 97 577 769 odious 13 19 37 73 97 109 193 433 487 577 + 28311553 63700993 113246209 258280327 pancake 37 panconsummate 37 73 257 pandigital 19 pernicious 13 17 19 37 73 97 109 193 257 433 + 1492993 1769473 1990657 8503057 Perrin 17 plaindrome 13 17 19 37 257 577 1459 3457 3889 12289 prime 13 17 19 37 73 97 109 163 193 257 + 206158430209 251048476873 347892350977 880602513409 primeval 13 37 Proth 13 17 97 193 257 577 769 1153 3457 10369 + 123834728449 206158430209 347892350977 880602513409 repfigit 19 repunit 13 73 self 97 2593 18433 star 13 37 73 433 strong prime 17 37 97 163 487 769 1297 3457 39367 52489 + 8503057 28311553 71663617 86093443 super-d 19 769 10369 17497 139969 331777 tribonacci 13 truncatable prime 13 17 37 73 97 twin 13 17 19 73 109 193 433 1153 2593 65537 + 995329 57395629 63700993 169869313 uban 13 17 19 37 73 97 Ulam 13 97 10369 629857 1990657 upside-down 19 37 73 weak prime 13 19 73 109 193 433 577 1153 1459 2593 + 14155777 19131877 57395629 63700993 Woodall 17