<p>@HarryJones, fibonocci sequence is starting with 1,1, and adding previous 2 terms, so you get, 1,1,2,3,5,8,13,21,34… and the amount of exclamation marks I used was 5, clear proof that it was a “■■■■■” number, </p>
<p>a sexy prime means that when you add 6 to it it’s still a prime, and there is no need for a proof to an infinite amount of perfect numbers it’s corollary, since there infinite amount of primes in form of 2^n-1, and if you multiply that by 2^{n-1} you get a prime, examples include (2^2-1)(2^1), (2^3-1)(2^2), (2^5-1)(2^4)…(2^n-1)(2^{n-1})</p>
<p>it retains property that the sums of it’s factors besides for N itself, are summation of N. E.g. factors of 28 are 1,2,4,7,14 and not including n itself or 28, those numbers add up to 28, neat?</p>
<p>and I apologize, 8128, :P</p>
<p>here’s a longer list of perfection, 6,
28,
496,
8128,
33550336,
8589869056,
137438691328,
2305843008139952128,
2658455991569831744654692615953842176,
191561942608236107294793378084303638130997321548169216,</p>
<p>131640364585696483372397534604587229102234723183869431
17783728128,</p>
<p>144740111546645244279463731260859884815736774914748358
89066354349131199152128,</p>
<p>2356272345726734706578954899670990498847754785839260071014302
7597506337283178622239730365539602600561360255566462503270175
0528925780432155433824984287771524270103944969186640286445341
2803383143979023683862403317143592235664321970310172071316352
7487298747400647801939587165936401087419375649057918549492160
555646976,</p>
<p>1410537837067120690632079580860631898814867435147156678388386
7599995486774265238011410419332903769025156195056870982932716
4087724366370087116731268159313652487450652439805877296207297
4467232951666582288469268077866528701889208678794514783645693
1392206037069506473607357237869517647305526682625328488638371
5072974324463835300053138429460296575143368065570759537328128, </p>
<p>5416252628436584741265446537439131614085649053903169578460392
0818387206994158534859198999921056719921919057390080263646159
2800138276054397462627889030573034455058270283951394752077690
4492443149486172943511312628083790493046274068171796046586734
8720992572190569465545299629919823431031092624244463547789635
4414813917198164416055867880921478866773213987566616247145517
2696430221755428178425481731961195165985555357393778892340514
6222324506715979193757372820860878214322052227584537552897476
2561793951766244263144803134469350852036575847982475360211728
8040378304860287362125931378999490033667394150374722496698402
8240806042108690077670395259231894666273615212775603535764707
9522501738583051710286030212348966478513639499289049732921451
07505979911456221519899345764984291328</p>
Bashing people who think they’re savvy is fun, :D</p>