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Proth数

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（最多15位数）

表格的数量k个⋅ 2n个+1，带k个奇数，n个>0和2n个>k个.更多

前600个Proth数字：
三,5,9,13,17,25,33,41,49,57,65,81,97,113,129,145,161,177,193,209,225,241,257,289,321,353,385,417,449,481,513,545,577,609,641,673,705,737,769,801,833,865,897,929,961,993,1025,1089,1153,1217,1281,1345,1409,1473,1537,1601,1665,1729,1793,1857,1921,1985,2049,2113,2177,2241,2305,2369,2433,2497,2561,2625,2689,2753,2817,2881,2945,3009,3073,3137,3201,3265,3329,3393,3457,3521,3585,3649,3713,3777,3841,3905,3969,4033,4097,4225,4353,4481,4609,4737,4865,4993,5121,5249,5377,5505,5633,5761,5889,6017,6145,6273,6401,6529,6657,6785,6913,7041,7169,7297,7425,7553,7681,7809,7937,8065,8193,8321,8449,8577,8705,8833,8961,9089,9217,9345,9473,9601,9729,9857,9985,10113,10241,10369,10497,10625,10753,10881,11009,11137,11265,11393,11521,11649,11777,11905,12033,12161,12289,12417,12545,12673,12801,12929,13057,13185,13313,13441,13569,13697,13825,13953,14081,14209,14337,14465,14593,14721,14849,14977,15105,15233,15361,15489,15617,15745,15873,16001,16129,16257,16385,16641,16897,17153,17409,17665,17921,18177,18433,18689,18945,19201,19457,19713,19969,20225,20481,20737,20993,21249,21505,21761,22017,22273,22529,22785,23041,23297,23553,23809,24065,24321,24577,24833,25089,25345,25601,25857,26113,26369,26625,26881,27137,27393,27649,27905,28161,28417,28673,28929,29185,29441,29697,29953,30209,30465,30721,30977,31233,31489,31745,32001,32257,32513,32769,33025,33281,33537,33793,34049,34305,34561,34817,35073,35329,35585,35841,36097,36353,36609,36865,37121,37377,37633,37889,38145,38401,38657,38913,39169,39425,39681,39937,40193,40449,40705,40961,41217,41473,41729,41985,42241,42497,42753,43009,43265,43521,43777,44033,44289,44545,44801,45057,45313,45569,45825,46081,46337,46593,46849,47105,47361,47617,47873,48129,48385,48641,48897,49153,49409,49665,49921,50177,50433,50689,50945,51201,51457,51713,51969,52225,52481,52737,52993,53249,53505,53761,54017,54273,54529,54785,55041,55297,55553,55809,56065,56321,56577,56833,57089,57345,57601,57857,58113,58369,58625,58881,59137,59393,59649,59905,60161,60417,60673,60929,61185,61441,61697,61953,62209,62465,62721,62977,63233,63489,63745,64001,64257,64513,64769,65025,65281,65537,66049,66561,67073,67585,68097,68609,69121,69633,70145,70657,71169,71681,72193,72705,73217,73729,74241,74753,75265,75777,76289,76801,77313,77825,78337,78849,79361,79873,80385,80897,81409,81921,82433,82945,83457,83969,84481,84993,85505,86017,86529,87041,87553,88065,88577,89089,89601,90113,90625,91137,91649,92161,92673,93185,93697,94209,94721,95233,95745,96257,96769,97281,97793,98305,98817,99329,99841,100353,100865,101377,101889,102401,102913,103425,103937,104449,104961,105473,105985,106497,107009,107521,108033,108545,109057,109569,110081,110593,111105,111617,112129,112641,113153,113665,114177,114689,115201,115713,116225,116737,117249,117761,118273,118785,119297,119809,120321,120833,121345,121857,122369,122881,123393,123905,124417,124929,125441,125953,126465,126977,127489,128001,128513,129025,129537,130049,130561,131073,131585,132097,132609,133121,133633,134145,134657,135169,135681,136193,136705,137217,137729,138241,138753,139265,139777,140289,140801,141313,141825,142337,142849,143361,143873,144385,144897,145409,145921,146433,146945,147457,147969,148481,148993,149505,150017,150529,151041,151553,152065,152577,153089,153601,154113,154625,155137,155649,156161,156673,157185,157697,158209,158721,159233,159745,160257,160769,161281,161793,162305,162817,163329,163841,164353,164865,165377,165889,166401,166913,167425,167937,168449,168961,169473,169985,170497,171009,171521,172033,172545,173057,173569,174081,174593,175105,175617,176129,176641.

剩余物的分配当这个家族中的数字除以n个=2, 3,..., 11.（我考虑了1477961个值，从3到999999 668225）。

n个 0  1 
201477961 2 
三492654492653492654 3 
40147796001 4 
5295593295591295592295593295592 5 
6049265304926540492654 6 
7211131211137211137211138211137211138211143 7 
801477958010200 8 
9164218164217164218164219164218164218164217164218164218 9 
1002955910295593029559302955920295592 10 
11134360134359134360134361134360134361134360134361134360134360134359

上表的图示
摩托车
想象一下用一个数字来划分这个家庭的成员n个并计算余数。如果它们均匀分布，则每个余数从0到n个-1将在大约（1）中获得/n个)-第个案例。此结果由白色方块表示。红色（分别为蓝色）方块表示剩余物，其出现频率高于（分别低于）1/n个.