^         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：
<hidden>
<code cpp>
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)
</code>
</hidden>