# Primes p<2^2048 of the form x^k-x^j+1 where x=2^8. # These primes allow easy modular reduction. #. # Generated by Joerg Arndt, 2007-September-23 # 2^24-2^8+1 == 2^(8*3)-2^(8*1)+1 2^40-2^32+1 == 2^(8*5)-2^(8*4)+1 2^56-2^24+1 == 2^(8*7)-2^(8*3)+1 2^56-2^32+1 == 2^(8*7)-2^(8*4)+1 2^64-2^24+1 == 2^(8*8)-2^(8*3)+1 2^64-2^32+1 == 2^(32*2)-2^(32*1)+1 2^64-2^40+1 == 2^(8*8)-2^(8*5)+1 2^80-2^48+1 == 2^(16*5)-2^(16*3)+1 2^80-2^72+1 == 2^(8*10)-2^(8*9)+1 2^96-2^32+1 == 2^(32*3)-2^(32*1)+1 2^136-2^88+1 == 2^(8*17)-2^(8*11)+1 2^136-2^112+1 == 2^(8*17)-2^(8*14)+1 2^176-2^48+1 == 2^(16*11)-2^(16*3)+1 2^176-2^80+1 == 2^(16*11)-2^(16*5)+1 2^200-2^184+1 == 2^(8*25)-2^(8*23)+1 2^208-2^24+1 == 2^(8*26)-2^(8*3)+1 2^216-2^72+1 == 2^(8*27)-2^(8*9)+1 == 2^((8*9)*3)-2^((8*9)*1)+1 2^216-2^152+1 == 2^(8*27)-2^(8*19)+1 2^224-2^96+1 == 2^(32*7)-2^(32*3)+1 2^224-2^168+1 == 2^(8*28)-2^(8*21)+1 == 2^((8*7)*4)-2^((8*7)*3)+1 2^256-2^168+1 == 2^(8*32)-2^(8*21)+1 2^280-2^168+1 == 2^(8*35)-2^(8*21)+1 == 2^((8*7)*5)-2^((8*7)*3)+1 2^296-2^80+1 == 2^(8*37)-2^(8*10)+1 2^296-2^192+1 == 2^(8*37)-2^(8*24)+1 2^296-2^232+1 == 2^(8*37)-2^(8*29)+1 2^304-2^184+1 == 2^(8*38)-2^(8*23)+1 2^320-2^288+1 == 2^(32*10)-2^(32*9)+1 2^344-2^336+1 == 2^(8*43)-2^(8*42)+1 2^352-2^120+1 == 2^(8*44)-2^(8*15)+1 2^360-2^272+1 == 2^(8*45)-2^(8*34)+1 2^368-2^336+1 == 2^(16*23)-2^(16*21)+1 2^376-2^344+1 == 2^(8*47)-2^(8*43)+1 2^384-2^80+1 == 2^(16*24)-2^(16*5)+1 2^392-2^280+1 == 2^(8*49)-2^(8*35)+1 == 2^((8*7)*7)-2^((8*7)*5)+1 2^400-2^160+1 == 2^(16*25)-2^(16*10)+1 == 2^((16*5)*5)-2^((16*5)*2)+1 2^424-2^288+1 == 2^(8*53)-2^(8*36)+1 2^424-2^296+1 == 2^(8*53)-2^(8*37)+1 2^440-2^112+1 == 2^(8*55)-2^(8*14)+1 2^456-2^432+1 == 2^(8*57)-2^(8*54)+1 == 2^((8*3)*19)-2^((8*3)*18)+1 2^488-2^240+1 == 2^(8*61)-2^(8*30)+1 2^488-2^424+1 == 2^(8*61)-2^(8*53)+1 2^488-2^464+1 == 2^(8*61)-2^(8*58)+1 2^504-2^168+1 == 2^(8*63)-2^(8*21)+1 == 2^((8*21)*3)-2^((8*21)*1)+1 2^504-2^192+1 == 2^(8*63)-2^(8*24)+1 == 2^((8*3)*21)-2^((8*3)*8)+1 2^504-2^392+1 == 2^(8*63)-2^(8*49)+1 == 2^((8*7)*9)-2^((8*7)*7)+1 2^512-2^32+1 == 2^(32*16)-2^(32*1)+1 2^512-2^288+1 == 2^(32*16)-2^(32*9)+1 2^520-2^424+1 == 2^(8*65)-2^(8*53)+1 2^528-2^336+1 == 2^(16*33)-2^(16*21)+1 == 2^((16*3)*11)-2^((16*3)*7)+1 2^536-2^56+1 == 2^(8*67)-2^(8*7)+1 2^544-2^32+1 == 2^(32*17)-2^(32*1)+1 2^544-2^96+1 == 2^(32*17)-2^(32*3)+1 2^544-2^184+1 == 2^(8*68)-2^(8*23)+1 2^544-2^304+1 == 2^(16*34)-2^(16*19)+1 2^552-2^528+1 == 2^(8*69)-2^(8*66)+1 == 2^((8*3)*23)-2^((8*3)*22)+1 2^560-2^112+1 == 2^(16*35)-2^(16*7)+1 == 2^((16*7)*5)-2^((16*7)*1)+1 2^576-2^240+1 == 2^(16*36)-2^(16*15)+1 == 2^((16*3)*12)-2^((16*3)*5)+1 2^576-2^264+1 == 2^(8*72)-2^(8*33)+1 == 2^((8*3)*24)-2^((8*3)*11)+1 2^576-2^512+1 == 2^(64*9)-2^(64*8)+1 2^584-2^376+1 == 2^(8*73)-2^(8*47)+1 2^584-2^568+1 == 2^(8*73)-2^(8*71)+1 2^600-2^264+1 == 2^(8*75)-2^(8*33)+1 == 2^((8*3)*25)-2^((8*3)*11)+1 2^600-2^360+1 == 2^(8*75)-2^(8*45)+1 == 2^((8*15)*5)-2^((8*15)*3)+1 2^608-2^536+1 == 2^(8*76)-2^(8*67)+1 2^616-2^216+1 == 2^(8*77)-2^(8*27)+1 2^624-2^56+1 == 2^(8*78)-2^(8*7)+1 2^624-2^104+1 == 2^(8*78)-2^(8*13)+1 == 2^((8*13)*6)-2^((8*13)*1)+1 2^648-2^464+1 == 2^(8*81)-2^(8*58)+1 2^664-2^368+1 == 2^(8*83)-2^(8*46)+1 2^664-2^560+1 == 2^(8*83)-2^(8*70)+1 2^664-2^576+1 == 2^(8*83)-2^(8*72)+1 2^672-2^192+1 == 2^(32*21)-2^(32*6)+1 == 2^((32*3)*7)-2^((32*3)*2)+1 2^672-2^560+1 == 2^(16*42)-2^(16*35)+1 == 2^((16*7)*6)-2^((16*7)*5)+1 2^680-2^592+1 == 2^(8*85)-2^(8*74)+1 2^688-2^96+1 == 2^(16*43)-2^(16*6)+1 2^696-2^80+1 == 2^(8*87)-2^(8*10)+1 2^712-2^88+1 == 2^(8*89)-2^(8*11)+1 2^712-2^208+1 == 2^(8*89)-2^(8*26)+1 2^712-2^256+1 == 2^(8*89)-2^(8*32)+1 2^744-2^392+1 == 2^(8*93)-2^(8*49)+1 2^776-2^256+1 == 2^(8*97)-2^(8*32)+1 2^784-2^48+1 == 2^(16*49)-2^(16*3)+1 2^792-2^600+1 == 2^(8*99)-2^(8*75)+1 == 2^((8*3)*33)-2^((8*3)*25)+1 2^800-2^8+1 == 2^(8*100)-2^(8*1)+1 2^824-2^408+1 == 2^(8*103)-2^(8*51)+1 2^832-2^72+1 == 2^(8*104)-2^(8*9)+1 2^832-2^432+1 == 2^(16*52)-2^(16*27)+1 2^832-2^448+1 == 2^(64*13)-2^(64*7)+1 2^856-2^560+1 == 2^(8*107)-2^(8*70)+1 2^864-2^632+1 == 2^(8*108)-2^(8*79)+1 2^872-2^840+1 == 2^(8*109)-2^(8*105)+1 2^880-2^368+1 == 2^(16*55)-2^(16*23)+1 2^912-2^32+1 == 2^(16*57)-2^(16*2)+1 2^936-2^512+1 == 2^(8*117)-2^(8*64)+1 2^936-2^600+1 == 2^(8*117)-2^(8*75)+1 == 2^((8*3)*39)-2^((8*3)*25)+1 2^944-2^696+1 == 2^(8*118)-2^(8*87)+1 2^944-2^784+1 == 2^(16*59)-2^(16*49)+1 2^952-2^16+1 == 2^(8*119)-2^(8*2)+1 2^960-2^600+1 == 2^(8*120)-2^(8*75)+1 == 2^((8*15)*8)-2^((8*15)*5)+1 2^968-2^296+1 == 2^(8*121)-2^(8*37)+1 2^968-2^928+1 == 2^(8*121)-2^(8*116)+1 2^968-2^944+1 == 2^(8*121)-2^(8*118)+1 2^976-2^664+1 == 2^(8*122)-2^(8*83)+1 2^984-2^32+1 == 2^(8*123)-2^(8*4)+1 2^984-2^168+1 == 2^(8*123)-2^(8*21)+1 == 2^((8*3)*41)-2^((8*3)*7)+1 2^984-2^680+1 == 2^(8*123)-2^(8*85)+1 2^992-2^408+1 == 2^(8*124)-2^(8*51)+1 2^992-2^832+1 == 2^(32*31)-2^(32*26)+1 2^1008-2^144+1 == 2^(16*63)-2^(16*9)+1 == 2^((16*9)*7)-2^((16*9)*1)+1 2^1008-2^776+1 == 2^(8*126)-2^(8*97)+1 2^1024-2^856+1 == 2^(8*128)-2^(8*107)+1 2^1024-2^880+1 == 2^(16*64)-2^(16*55)+1 2^1032-2^312+1 == 2^(8*129)-2^(8*39)+1 == 2^((8*3)*43)-2^((8*3)*13)+1 2^1032-2^752+1 == 2^(8*129)-2^(8*94)+1 2^1040-2^464+1 == 2^(16*65)-2^(16*29)+1 2^1040-2^592+1 == 2^(16*65)-2^(16*37)+1 2^1040-2^624+1 == 2^(16*65)-2^(16*39)+1 == 2^((16*13)*5)-2^((16*13)*3)+1 2^1048-2^160+1 == 2^(8*131)-2^(8*20)+1 2^1048-2^528+1 == 2^(8*131)-2^(8*66)+1 2^1048-2^1040+1 == 2^(8*131)-2^(8*130)+1 2^1056-2^920+1 == 2^(8*132)-2^(8*115)+1 2^1064-2^432+1 == 2^(8*133)-2^(8*54)+1 2^1064-2^616+1 == 2^(8*133)-2^(8*77)+1 == 2^((8*7)*19)-2^((8*7)*11)+1 2^1064-2^920+1 == 2^(8*133)-2^(8*115)+1 2^1088-2^608+1 == 2^(32*34)-2^(32*19)+1 2^1096-2^688+1 == 2^(8*137)-2^(8*86)+1 2^1104-2^272+1 == 2^(16*69)-2^(16*17)+1 2^1104-2^360+1 == 2^(8*138)-2^(8*45)+1 == 2^((8*3)*46)-2^((8*3)*15)+1 2^1104-2^1088+1 == 2^(16*69)-2^(16*68)+1 2^1120-2^840+1 == 2^(8*140)-2^(8*105)+1 == 2^((8*35)*4)-2^((8*35)*3)+1 2^1136-2^1104+1 == 2^(16*71)-2^(16*69)+1 2^1144-2^1064+1 == 2^(8*143)-2^(8*133)+1 2^1160-2^560+1 == 2^(8*145)-2^(8*70)+1 == 2^((8*5)*29)-2^((8*5)*14)+1 2^1160-2^912+1 == 2^(8*145)-2^(8*114)+1 2^1184-2^768+1 == 2^(32*37)-2^(32*24)+1 2^1192-2^128+1 == 2^(8*149)-2^(8*16)+1 2^1192-2^1080+1 == 2^(8*149)-2^(8*135)+1 2^1208-2^288+1 == 2^(8*151)-2^(8*36)+1 2^1216-2^616+1 == 2^(8*152)-2^(8*77)+1 2^1216-2^880+1 == 2^(16*76)-2^(16*55)+1 2^1224-2^384+1 == 2^(8*153)-2^(8*48)+1 == 2^((8*3)*51)-2^((8*3)*16)+1 2^1232-2^200+1 == 2^(8*154)-2^(8*25)+1 2^1264-2^448+1 == 2^(16*79)-2^(16*28)+1 2^1272-2^56+1 == 2^(8*159)-2^(8*7)+1 2^1288-2^1216+1 == 2^(8*161)-2^(8*152)+1 2^1296-2^248+1 == 2^(8*162)-2^(8*31)+1 2^1296-2^896+1 == 2^(16*81)-2^(16*56)+1 2^1304-2^208+1 == 2^(8*163)-2^(8*26)+1 2^1304-2^584+1 == 2^(8*163)-2^(8*73)+1 2^1312-2^496+1 == 2^(16*82)-2^(16*31)+1 2^1336-2^32+1 == 2^(8*167)-2^(8*4)+1 2^1336-2^696+1 == 2^(8*167)-2^(8*87)+1 2^1336-2^1048+1 == 2^(8*167)-2^(8*131)+1 2^1352-2^320+1 == 2^(8*169)-2^(8*40)+1 2^1352-2^712+1 == 2^(8*169)-2^(8*89)+1 2^1360-2^608+1 == 2^(16*85)-2^(16*38)+1 2^1376-2^32+1 == 2^(32*43)-2^(32*1)+1 2^1376-2^152+1 == 2^(8*172)-2^(8*19)+1 2^1384-2^88+1 == 2^(8*173)-2^(8*11)+1 2^1384-2^544+1 == 2^(8*173)-2^(8*68)+1 2^1400-2^32+1 == 2^(8*175)-2^(8*4)+1 2^1416-2^1176+1 == 2^(8*177)-2^(8*147)+1 == 2^((8*3)*59)-2^((8*3)*49)+1 2^1432-2^400+1 == 2^(8*179)-2^(8*50)+1 2^1448-2^840+1 == 2^(8*181)-2^(8*105)+1 2^1464-2^1368+1 == 2^(8*183)-2^(8*171)+1 == 2^((8*3)*61)-2^((8*3)*57)+1 2^1480-2^88+1 == 2^(8*185)-2^(8*11)+1 2^1488-2^248+1 == 2^(8*186)-2^(8*31)+1 == 2^((8*31)*6)-2^((8*31)*1)+1 2^1488-2^536+1 == 2^(8*186)-2^(8*67)+1 2^1512-2^32+1 == 2^(8*189)-2^(8*4)+1 2^1520-2^544+1 == 2^(16*95)-2^(16*34)+1 2^1528-2^416+1 == 2^(8*191)-2^(8*52)+1 2^1544-2^248+1 == 2^(8*193)-2^(8*31)+1 2^1544-2^264+1 == 2^(8*193)-2^(8*33)+1 2^1544-2^296+1 == 2^(8*193)-2^(8*37)+1 2^1544-2^904+1 == 2^(8*193)-2^(8*113)+1 2^1560-2^80+1 == 2^(8*195)-2^(8*10)+1 == 2^((8*5)*39)-2^((8*5)*2)+1 2^1560-2^104+1 == 2^(8*195)-2^(8*13)+1 == 2^((8*13)*15)-2^((8*13)*1)+1 2^1560-2^1344+1 == 2^(8*195)-2^(8*168)+1 == 2^((8*3)*65)-2^((8*3)*56)+1 2^1568-2^1368+1 == 2^(8*196)-2^(8*171)+1 2^1576-2^264+1 == 2^(8*197)-2^(8*33)+1 2^1592-2^616+1 == 2^(8*199)-2^(8*77)+1 2^1600-2^1272+1 == 2^(8*200)-2^(8*159)+1 2^1608-2^80+1 == 2^(8*201)-2^(8*10)+1 2^1608-2^464+1 == 2^(8*201)-2^(8*58)+1 2^1608-2^1136+1 == 2^(8*201)-2^(8*142)+1 2^1608-2^1256+1 == 2^(8*201)-2^(8*157)+1 2^1616-2^1040+1 == 2^(16*101)-2^(16*65)+1 2^1616-2^1512+1 == 2^(8*202)-2^(8*189)+1 2^1624-2^600+1 == 2^(8*203)-2^(8*75)+1 2^1624-2^688+1 == 2^(8*203)-2^(8*86)+1 2^1624-2^1032+1 == 2^(8*203)-2^(8*129)+1 2^1632-2^200+1 == 2^(8*204)-2^(8*25)+1 2^1656-2^152+1 == 2^(8*207)-2^(8*19)+1 2^1656-2^624+1 == 2^(8*207)-2^(8*78)+1 == 2^((8*3)*69)-2^((8*3)*26)+1 2^1656-2^888+1 == 2^(8*207)-2^(8*111)+1 == 2^((8*3)*69)-2^((8*3)*37)+1 2^1656-2^1544+1 == 2^(8*207)-2^(8*193)+1 2^1664-2^256+1 == 2^(128*13)-2^(128*2)+1 2^1664-2^840+1 == 2^(8*208)-2^(8*105)+1 2^1680-2^312+1 == 2^(8*210)-2^(8*39)+1 == 2^((8*3)*70)-2^((8*3)*13)+1 2^1680-2^1592+1 == 2^(8*210)-2^(8*199)+1 2^1696-2^1384+1 == 2^(8*212)-2^(8*173)+1 2^1696-2^1608+1 == 2^(8*212)-2^(8*201)+1 2^1712-2^1352+1 == 2^(8*214)-2^(8*169)+1 2^1720-2^512+1 == 2^(8*215)-2^(8*64)+1 2^1736-2^1528+1 == 2^(8*217)-2^(8*191)+1 2^1744-2^848+1 == 2^(16*109)-2^(16*53)+1 2^1776-2^128+1 == 2^(16*111)-2^(16*8)+1 2^1800-2^864+1 == 2^(8*225)-2^(8*108)+1 == 2^((8*9)*25)-2^((8*9)*12)+1 2^1824-2^936+1 == 2^(8*228)-2^(8*117)+1 == 2^((8*3)*76)-2^((8*3)*39)+1 2^1824-2^1448+1 == 2^(8*228)-2^(8*181)+1 2^1832-2^752+1 == 2^(8*229)-2^(8*94)+1 2^1832-2^1136+1 == 2^(8*229)-2^(8*142)+1 2^1840-2^1760+1 == 2^(16*115)-2^(16*110)+1 == 2^((16*5)*23)-2^((16*5)*22)+1 2^1848-2^576+1 == 2^(8*231)-2^(8*72)+1 == 2^((8*3)*77)-2^((8*3)*24)+1 2^1856-2^1056+1 == 2^(32*58)-2^(32*33)+1 2^1864-2^752+1 == 2^(8*233)-2^(8*94)+1 2^1888-2^840+1 == 2^(8*236)-2^(8*105)+1 2^1896-2^296+1 == 2^(8*237)-2^(8*37)+1 2^1912-2^488+1 == 2^(8*239)-2^(8*61)+1 2^1920-2^384+1 == 2^(128*15)-2^(128*3)+1 == 2^((128*3)*5)-2^((128*3)*1)+1 2^1936-2^336+1 == 2^(16*121)-2^(16*21)+1 2^1960-2^808+1 == 2^(8*245)-2^(8*101)+1 2^1960-2^1048+1 == 2^(8*245)-2^(8*131)+1 2^1960-2^1440+1 == 2^(8*245)-2^(8*180)+1 == 2^((8*5)*49)-2^((8*5)*36)+1 2^1968-2^224+1 == 2^(16*123)-2^(16*14)+1 2^1968-2^1488+1 == 2^(16*123)-2^(16*93)+1 == 2^((16*3)*41)-2^((16*3)*31)+1 2^1976-2^728+1 == 2^(8*247)-2^(8*91)+1 == 2^((8*13)*19)-2^((8*13)*7)+1 2^1984-2^544+1 == 2^(32*62)-2^(32*17)+1 2^2008-2^1368+1 == 2^(8*251)-2^(8*171)+1 2^2032-2^1560+1 == 2^(8*254)-2^(8*195)+1 ## the following are strong pseudo primes to all prime bases<100 ## i.e. the bases [2, 3, 5, 7, 11, ..., 89, 97]: # 2^576-2^512+1 == 2^(64*9)-2^(64*8)+1 # 2^832-2^448+1 == 2^(64*13)-2^(64*7)+1 # 2^1664-2^256+1 == 2^(128*13)-2^(128*2)+1 # 2^1920-2^384+1 == 2^(128*15)-2^(128*3)+1 == 2^((128*3)*5)-2^((128*3)*1)+1 # 2^4288-2^3776+1 == 2^(64*67)-2^(64*59)+1 # 2^4544-2^3008+1 == 2^(64*71)-2^(64*47)+1 # 2^4928-2^3584+1 == 2^(64*77)-2^(64*56)+1 == 2^((64*7)*11)-2^((64*7)*8)+1 # 2^5440-2^320+1 == 2^(64*85)-2^(64*5)+1 == 2^((64*5)*17)-2^((64*5)*1)+1 # 2^5696-2^704+1 == 2^(64*89)-2^(64*11)+1 # 2^5824-2^640+1 == 2^(64*91)-2^(64*10)+1 # 2^6272-2^5760+1 == 2^(128*49)-2^(128*45)+1 # 2^6336-2^2240+1 == 2^(64*99)-2^(64*35)+1 # 2^7488-2^3200+1 == 2^(64*117)-2^(64*50)+1 # 2^8640-2^1920+1 == 2^(64*135)-2^(64*30)+1 == 2^((64*15)*9)-2^((64*15)*2)+1