NTT 模数 表达式 原根 NTT 模数 表达式 原根
$12289$ $3\times2^{12}+1$ $11$ $13313$ $13\times2^{10}+1$ $3$
$15361$ $15\times2^{10}+1$ $7$ $18433$ $9\times2^{11}+1$ $5$
$19457$ $19\times2^{10}+1$ $3$ $25601$ $25\times2^{10}+1$ $3$
$37889$ $37\times2^{10}+1$ $3$ $39937$ $39\times2^{10}+1$ $5$
$40961$ $5\times2^{13}+1$ $3$ $50177$ $49\times2^{10}+1$ $3$
$58369$ $57\times2^{10}+1$ $7$ $59393$ $29\times2^{11}+1$ $5$
$61441$ $15\times2^{12}+1$ $17$ $64513$ $63\times2^{10}+1$ $5$
$65537$ $1\times2^{16}+1$ $3$ $70657$ $69\times2^{10}+1$ $7$
$76801$ $75\times2^{10}+1$ $17$ $79873$ $39\times2^{11}+1$ $7$
$80897$ $79\times2^{10}+1$ $3$ $83969$ $41\times2^{11}+1$ $3$
$86017$ $21\times2^{12}+1$ $5$ $87041$ $85\times2^{10}+1$ $3$
$95233$ $93\times2^{10}+1$ $5$ $101377$ $99\times2^{10}+1$ $5$
$114689$ $7\times2^{14}+1$ $3$ $119809$ $117\times2^{10}+1$ $11$
$120833$ $59\times2^{11}+1$ $3$ $133121$ $65\times2^{11}+1$ $3$
$147457$ $9\times2^{14}+1$ $10$ $151553$ $37\times2^{12}+1$ $3$
$163841$ $5\times2^{15}+1$ $3$ $176129$ $43\times2^{12}+1$ $3$
$184321$ $45\times2^{12}+1$ $13$ $188417$ $23\times2^{13}+1$ $3$
$202753$ $99\times2^{11}+1$ $10$ $249857$ $61\times2^{12}+1$ $3$
$270337$ $33\times2^{13}+1$ $10$ $286721$ $35\times2^{13}+1$ $11$
$307201$ $75\times2^{12}+1$ $14$ $319489$ $39\times2^{13}+1$ $23$
$331777$ $81\times2^{12}+1$ $5$ $380929$ $93\times2^{12}+1$ $7$
$417793$ $51\times2^{13}+1$ $5$ $430081$ $105\times2^{12}+1$ $13$
$471041$ $115\times2^{12}+1$ $6$ $557057$ $17\times2^{15}+1$ $3$
$638977$ $39\times2^{14}+1$ $7$ $737281$ $45\times2^{14}+1$ $11$
$778241$ $95\times2^{13}+1$ $6$ $786433$ $3\times2^{18}+1$ $10$
$925697$ $113\times2^{13}+1$ $3$ $974849$ $119\times2^{13}+1$ $3$
$1032193$ $63\times2^{14}+1$ $11$ $1097729$ $67\times2^{14}+1$ $3$
$1130497$ $69\times2^{14}+1$ $5$ $1146881$ $35\times2^{15}+1$ $3$
$1179649$ $9\times2^{17}+1$ $19$ $1196033$ $73\times2^{14}+1$ $3$
$1376257$ $21\times2^{16}+1$ $5$ $1589249$ $97\times2^{14}+1$ $3$
$1720321$ $105\times2^{14}+1$ $17$ $1769473$ $27\times2^{16}+1$ $5$
$1785857$ $109\times2^{14}+1$ $3$ $2424833$ $37\times2^{16}+1$ $3$
$2654209$ $81\times2^{15}+1$ $11$ $2752513$ $21\times2^{17}+1$ $20$
$3604481$ $55\times2^{16}+1$ $3$ $3735553$ $57\times2^{16}+1$ $5$
$5308417$ $81\times2^{16}+1$ $5$ $5767169$ $11\times2^{19}+1$ $3$
$6684673$ $51\times2^{17}+1$ $5$ $6750209$ $103\times2^{16}+1$ $3$
$6946817$ $53\times2^{17}+1$ $3$ $7340033$ $7\times2^{20}+1$ $3$
$7667713$ $117\times2^{16}+1$ $10$ $8257537$ $63\times2^{17}+1$ $5$
$8519681$ $65\times2^{17}+1$ $3$ $8650753$ $33\times2^{18}+1$ $10$
$10223617$ $39\times2^{18}+1$ $5$ $11272193$ $43\times2^{18}+1$ $3$
$12451841$ $95\times2^{17}+1$ $3$ $13238273$ $101\times2^{17}+1$ $3$
$13631489$ $13\times2^{20}+1$ $15$ $14155777$ $27\times2^{19}+1$ $7$
$14942209$ $57\times2^{18}+1$ $11$ $16515073$ $63\times2^{18}+1$ $5$
$21495809$ $41\times2^{19}+1$ $3$ $22806529$ $87\times2^{18}+1$ $13$
$23068673$ $11\times2^{21}+1$ $3$ $26214401$ $25\times2^{20}+1$ $3$
$27000833$ $103\times2^{18}+1$ $3$ $28311553$ $27\times2^{20}+1$ $5$
$29884417$ $57\times2^{19}+1$ $5$ $36175873$ $69\times2^{19}+1$ $7$
$37224449$ $71\times2^{19}+1$ $3$ $40370177$ $77\times2^{19}+1$ $3$
$69206017$ $33\times2^{21}+1$ $5$ $70254593$ $67\times2^{20}+1$ $3$
$81788929$ $39\times2^{21}+1$ $7$ $101711873$ $97\times2^{20}+1$ $3$
$104857601$ $25\times2^{22}+1$ $3$ $111149057$ $53\times2^{21}+1$ $3$
$113246209$ $27\times2^{22}+1$ $7$ $120586241$ $115\times2^{20}+1$ $6$
$132120577$ $63\times2^{21}+1$ $5$ $136314881$ $65\times2^{21}+1$ $3$
$138412033$ $33\times2^{22}+1$ $5$ $155189249$ $37\times2^{22}+1$ $6$
$163577857$ $39\times2^{22}+1$ $23$ $167772161$ $5\times2^{25}+1$ $3$
$169869313$ $81\times2^{21}+1$ $5$ $186646529$ $89\times2^{21}+1$ $3$
$199229441$ $95\times2^{21}+1$ $3$ $211812353$ $101\times2^{21}+1$ $3$
$230686721$ $55\times2^{22}+1$ $6$ $249561089$ $119\times2^{21}+1$ $3$
$377487361$ $45\times2^{23}+1$ $7$ $415236097$ $99\times2^{22}+1$ $5$
$469762049$ $7\times2^{26}+1$ $3$ $595591169$ $71\times2^{23}+1$ $3$
$645922817$ $77\times2^{23}+1$ $3$ $754974721$ $45\times2^{24}+1$ $11$
$880803841$ $105\times2^{23}+1$ $26$ $897581057$ $107\times2^{23}+1$ $3$
$998244353$ $119\times2^{23}+1$ $3$ $1107296257$ $33\times2^{25}+1$ $10$
$1224736769$ $73\times2^{24}+1$ $3$ $1711276033$ $51\times2^{25}+1$ $29$
$1811939329$ $27\times2^{26}+1$ $13$ $2013265921$ $15\times2^{27}+1$ $31$
$2113929217$ $63\times2^{25}+1$ $5$ $2281701377$ $17\times2^{27}+1$ $3$
$2483027969$ $37\times2^{26}+1$ $3$ $2717908993$ $81\times2^{25}+1$ $5$
$2885681153$ $43\times2^{26}+1$ $3$ $3221225473$ $3\times2^{30}+1$ $5$
$3489660929$ $13\times2^{28}+1$ $3$ $3892314113$ $29\times2^{27}+1$ $3$
$4630511617$ $69\times2^{26}+1$ $5$ $5838471169$ $87\times2^{26}+1$ $7$
$7717519361$ $115\times2^{26}+1$ $3$ $7918845953$ $59\times2^{27}+1$ $3$
$8858370049$ $33\times2^{28}+1$ $23$ $9529458689$ $71\times2^{27}+1$ $3$
$10871635969$ $81\times2^{27}+1$ $7$ $12348030977$ $23\times2^{29}+1$ $5$
$13555990529$ $101\times2^{27}+1$ $3$ $14092861441$ $105\times2^{27}+1$ $19$
$14361296897$ $107\times2^{27}+1$ $3$ $24159191041$ $45\times2^{29}+1$ $7$
$29796335617$ $111\times2^{28}+1$ $5$ $34896609281$ $65\times2^{29}+1$ $3$
$52613349377$ $49\times2^{30}+1$ $3$ $75161927681$ $35\times2^{31}+1$ $3$
$77309411329$ $9\times2^{33}+1$ $7$ $78383153153$ $73\times2^{30}+1$ $3$
$83751862273$ $39\times2^{31}+1$ $11$ $91268055041$ $85\times2^{30}+1$ $3$
$99857989633$ $93\times2^{30}+1$ $7$ $110595407873$ $103\times2^{30}+1$ $3$
$125627793409$ $117\times2^{30}+1$ $7$ $184683593729$ $43\times2^{32}+1$ $3$
$206158430209$ $3\times2^{36}+1$ $22$ $212600881153$ $99\times2^{31}+1$ $5$
$236223201281$ $55\times2^{32}+1$ $3$ $313532612609$ $73\times2^{32}+1$ $3$
$347892350977$ $81\times2^{32}+1$ $10$ $476741369857$ $111\times2^{32}+1$ $5$
$850403524609$ $99\times2^{33}+1$ $13$ $901943132161$ $105\times2^{33}+1$ $13$
$970662608897$ $113\times2^{33}+1$ $3$ $1288490188801$ $75\times2^{34}+1$ $11$
$1460288880641$ $85\times2^{34}+1$ $3$ $1700807049217$ $99\times2^{34}+1$ $7$
$2027224563713$ $59\times2^{35}+1$ $3$ $2061584302081$ $15\times2^{37}+1$ $7$
$2748779069441$ $5\times2^{39}+1$ $3$ $2783138807809$ $81\times2^{35}+1$ $11$
$4123168604161$ $15\times2^{38}+1$ $7$ $5566277615617$ $81\times2^{36}+1$ $5$
$5841155522561$ $85\times2^{36}+1$ $6$ $6597069766657$ $3\times2^{41}+1$ $5$
$8040178778113$ $117\times2^{36}+1$ $7$ $8658654068737$ $63\times2^{37}+1$ $5$
$12232066859009$ $89\times2^{37}+1$ $3$ $17317308137473$ $63\times2^{38}+1$ $5$
$23364622090241$ $85\times2^{38}+1$ $3$ $28862180229121$ $105\times2^{38}+1$ $19$
$29686813949953$ $27\times2^{40}+1$ $5$ $39582418599937$ $9\times2^{42}+1$ $5$
$44530220924929$ $81\times2^{39}+1$ $7$ $46179488366593$ $21\times2^{41}+1$ $11$
$50577534877697$ $23\times2^{41}+1$ $3$ $55525337202689$ $101\times2^{39}+1$ $3$
$62672162783233$ $57\times2^{40}+1$ $5$ $79164837199873$ $9\times2^{43}+1$ $5$
$96757023244289$ $11\times2^{43}+1$ $3$ $106652627894273$ $97\times2^{40}+1$ $3$
$113249697660929$ $103\times2^{40}+1$ $3$ $171523813933057$ $39\times2^{42}+1$ $5$
$215504279044097$ $49\times2^{42}+1$ $3$ $217703302299649$ $99\times2^{41}+1$ $7$
$255086697644033$ $29\times2^{43}+1$ $3$ $263882790666241$ $15\times2^{44}+1$ $7$
$321057395310593$ $73\times2^{42}+1$ $3$ $409018325532673$ $93\times2^{42}+1$ $7$
$435406604599297$ $99\times2^{42}+1$ $10$ $448600744132609$ $51\times2^{43}+1$ $11$
$474989023199233$ $27\times2^{44}+1$ $5$ $505775348776961$ $115\times2^{42}+1$ $3$
$659706976665601$ $75\times2^{43}+1$ $11$ $1108307720798209$ $63\times2^{44}+1$ $11$
$1178676464975873$ $67\times2^{44}+1$ $3$ $1231453023109121$ $35\times2^{45}+1$ $3$
$1284229581242369$ $73\times2^{44}+1$ $3$ $1337006139375617$ $19\times2^{46}+1$ $3$
$1636073302130689$ $93\times2^{44}+1$ $17$ $1899956092796929$ $27\times2^{46}+1$ $7$
$1952732650930177$ $111\times2^{44}+1$ $5$ $3553621580972033$ $101\times2^{45}+1$ $3$
$3799912185593857$ $27\times2^{47}+1$ $5$ $4186940278571009$ $119\times2^{45}+1$ $3$
$4222124650659841$ $15\times2^{48}+1$ $19$ $4925812092436481$ $35\times2^{47}+1$ $3$
$5559130790035457$ $79\times2^{46}+1$ $3$ $7881299347898369$ $7\times2^{50}+1$ $6$
$9147936743096321$ $65\times2^{47}+1$ $3$ $12947848928690177$ $23\times2^{49}+1$ $3$
$14214486323888129$ $101\times2^{47}+1$ $3$ $15621861207441409$ $111\times2^{47}+1$ $11$
$16044073672507393$ $57\times2^{48}+1$ $5$ $17169973579350017$ $61\times2^{48}+1$ $3$
$19703248369745921$ $35\times2^{49}+1$ $3$ $22799473113563137$ $81\times2^{48}+1$ $5$
$30399297484750849$ $27\times2^{50}+1$ $11$ $31525197391593473$ $7\times2^{52}+1$ $3$
$38280596832649217$ $17\times2^{51}+1$ $3$ $59109745109237761$ $105\times2^{49}+1$ $17$
$77687093572141057$ $69\times2^{50}+1$ $5$ $112589990684262401$ $25\times2^{52}+1$ $3$
$168884986026393601$ $75\times2^{51}+1$ $11$ $180143985094819841$ $5\times2^{55}+1$ $6$
$418834765345456129$ $93\times2^{52}+1$ $7$ $459367161991790593$ $51\times2^{53}+1$ $5$
$855683929200394241$ $95\times2^{53}+1$ $3$ $882705526964617217$ $49\times2^{54}+1$ $5$
$891712726219358209$ $99\times2^{53}+1$ $7$ $1261007895663738881$ $35\times2^{55}+1$ $6$
$1945555039024054273$ $27\times2^{56}+1$ $5$ $2053641430080946177$ $57\times2^{55}+1$ $7$
$2485986994308513793$ $69\times2^{55}+1$ $5$ $4179340454199820289$ $29\times2^{57}+1$ $3$
$6269010681299730433$ $87\times2^{56}+1$ $5$ $10232178353385766913$ $71\times2^{57}+1$ $3$
$10808639105689190401$ $75\times2^{57}+1$ $7$ $13690942867206307841$ $95\times2^{57}+1$ $3$
$15564440312192434177$ $27\times2^{59}+1$ $5$ $28534807239019462657$ $99\times2^{58}+1$ $5$
$29687728743626309633$ $103\times2^{58}+1$ $3$ $31417111000536580097$ $109\times2^{58}+1$ $3$
$35740566642812256257$ $31\times2^{60}+1$ $3$ $40928713413543067649$ $71\times2^{59}+1$ $3$
$51881467707308113921$ $45\times2^{60}+1$ $11$ $72634054790231359489$ $63\times2^{60}+1$ $34$
$84163269836299829249$ $73\times2^{60}+1$ $3$ $86469112845513523201$ $75\times2^{60}+1$ $14$
$122209679488325779457$ $53\times2^{61}+1$ $3$ $205220027820018761729$ $89\times2^{61}+1$ $3$
$219055085875300925441$ $95\times2^{61}+1$ $3$ $242113515967437864961$ $105\times2^{61}+1$ $11$
$484227031934875729921$ $105\times2^{62}+1$ $17$ $502673776008585281537$ $109\times2^{62}+1$ $3$

生成代码：

点击以显示 ⇲

点击以隐藏 ⇱ 

import sympy.ntheory as nth
import random
 
 
if __name__ == '__main__':
    output = list()
    for mult in range(1, 120, 2):
        for exp in range(10, 63):
            num = mult << exp | 1
            if nth.isprime(num):
                output.append((num, mult, exp, nth.residue_ntheory.primitive_root(num)))
    output.sort()
    print(len(output))
    print('^         NTT 模数          ^   表达式   ^         原根          ^         NTT 模数          ^   表达式   ^         原根          ^')
    for i in range(0, len(output), 2):
        num, mult, exp, pr_root = output[i]
        string = f'|  ${num}$  |  ${mult}\\times{2}^{{{exp}}}+1$  |  ${pr_root}$  '
        if i + 1 < len(output):
            num, mult, exp, pr_root = output[i + 1]
            string += f'|  ${num}$  |  ${mult}\\times{2}^{{{exp}}}+1$  |  ${pr_root}$  '
        string += '|'
        print(string)