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Carmichael 3 strong pseudoprimes: Difference between revisions
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This REXX version (pre-)generates
<lang rexx>/*REXX program calculates Carmichael 3─strong pseudoprimes (up to and including N). */
numeric digits
parse arg N .; if N=='' then N=61 /*allow user to specify for the search.*/
tell= N>0; N=abs(N) /*N>0? Then display Carmichael numbers*/
carms=0 ;
/*[↑] prime number memoization array. */
do p=3 to N by 2; pm=p-1; bot=0; top=0 /*step through some (odd) prime numbers*/
@.=0
do h3=2
gPM=g*pm; npsH3=((nps//h3)+h3)//h3 /*define a couple of shortcuts for pgm.*/
/* [↓] perform some weeding of D values*/
Line 1,336:
r=1+p*q%h3; if q*r//pm\==1 then iterate
if \isPrime(r) then iterate
carms=carms+1; @.q=r
if bot==0 then bot=q; bot=min(bot,q); top=max(top,q)
end /*d*/ /* [↑] find the minimum & the maximum.*/
end /*h3*/
do j=bot to top by 2 while tell; if @.j==0 then iterate; #=#','
end /*j*/
if #\=='' then say 'Carmichael numbers:' strip(#,, ",")
end /*p*/
say
say
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
isPrime: parse arg x; if !.x then return 1 /*X a known prime?*/
if x<
parse var x '' -1 _; if _==5 then return 0; if x// 7==0 then return 0
if x//11==0 then return 0; if x//13==0 then return 0
if x//17==0 then return 0; if x//19==0 then return 0
if x//23==0 then return 0;
if x//31==0 then return
c=x /* ___*/
b=1; do while b<=x; b=b*4; end /*these two lines compute integer √ X */
s=0; do while b>1; b=b%4; _=c-s-b; s=s%2; if _>=0 then do; c=_; s=s+b; end; end
do k=41 by 6 to s; parse var k '' -1 _
if _\==5 then if x// k ==0 then return 0
if _\==3 then if x//(k+2)==0 then return 0
end /*k*/ /*K will never be divisible by three.*/
!.x=1; return 1 /*Define a new prime (X). Indicate so.*/</lang>
'''output'''
<pre style="height:72ex">
Carmichael numbers: 3∙11∙17
Carmichael numbers: 5∙13∙17, 5∙17∙29, 5∙29∙73
Carmichael numbers: 7∙13∙19, 7∙19∙67, 7∙23∙41, 7∙31∙73, 7∙73∙103
Carmichael numbers: 13∙37∙61, 13∙61∙397, 13∙97∙421
Carmichael numbers: 17∙41∙233, 17∙353∙1201
Carmichael numbers: 19∙43∙409, 19∙199∙271
Carmichael numbers: 23∙199∙353
Carmichael numbers: 29∙113∙1093, 29∙197∙953
Carmichael numbers: 31∙61∙211, 31∙151∙1171, 31∙181∙331, 31∙271∙601, 31∙991∙15361
Carmichael numbers: 37∙73∙109, 37∙109∙2017, 37∙613∙1621
Carmichael numbers: 41∙61∙101, 41∙73∙137, 41∙101∙461, 41∙241∙521, 41∙881∙12041, 41∙1721∙35281
Carmichael numbers: 43∙127∙211, 43∙211∙337, 43∙271∙5827, 43∙433∙643, 43∙547∙673, 43∙631∙1597, 43∙3361∙3907
Carmichael numbers: 47∙1151∙1933, 47∙3359∙6073, 47∙3727∙5153
Carmichael numbers: 53∙79∙599, 53∙157∙521
Carmichael numbers: 59∙1451∙2089
Carmichael numbers: 61∙181∙1381, 61∙241∙421, 61∙271∙571, 61∙277∙2113, 61∙421∙12841, 61∙541∙3001, 61∙661∙2521, 61∙1301∙19841, 61∙3361∙4021
Carmichael numbers: 67∙331∙463, 67∙2311∙51613
Carmichael numbers: 71∙271∙521, 71∙421∙491, 71∙631∙701, 71∙701∙5531, 71∙911∙9241
Carmichael numbers: 73∙157∙2293, 73∙379∙523, 73∙601∙21937, 73∙937∙13681
Carmichael numbers: 79∙2237∙25247
Carmichael numbers: 83∙2953∙4019, 83∙6971∙289297
Carmichael numbers: 89∙353∙617, 89∙617∙3433, 89∙881∙7129, 89∙4049∙120121
Carmichael numbers: 97∙193∙1249, 97∙673∙769, 97∙769∙10657, 97∙1201∙38833, 97∙2113∙5857
Carmichael numbers: 101∙151∙251, 101∙1301∙43801
Carmichael numbers: 103∙647∙1361, 103∙1123∙6427, 103∙3571∙183907, 103∙3877∙4591, 103∙5407∙185641
Carmichael numbers: 107∙743∙1061, 107∙3181∙26183
Carmichael numbers: 109∙163∙379, 109∙229∙4993, 109∙241∙2389, 109∙379∙919, 109∙433∙2053, 109∙541∙2269, 109∙1297∙12853, 109∙1657∙6229, 109∙1801∙4789
Carmichael numbers: 113∙337∙449, 113∙827∙18691, 113∙6833∙85793, 113∙8737∙22961
Carmichael numbers: 127∙631∙26713, 127∙659∙1373, 127∙991∙3313, 127∙2143∙30241, 127∙16633∙422479
Carmichael numbers: 131∙491∙4021, 131∙521∙2731, 131∙571∙1871, 131∙911∙2341, 131∙1171∙38351, 131∙1301∙8971, 131∙4421∙115831, 131∙5851∙191621, 131∙17291∙1132561
Carmichael numbers: 137∙409∙14009, 137∙953∙5441, 137∙3673∙20129, 137∙5441∙11833
Carmichael numbers: 139∙691∙829, 139∙3359∙66701, 139∙4003∙92737, 139∙4969∙8971, 139∙17389∙21391
Carmichael numbers: 149∙593∙29453, 149∙1481∙3109
Carmichael numbers: 151∙211∙541, 151∙331∙3571, 151∙601∙751, 151∙701∙1451, 151∙751∙8101, 151∙2551∙192601, 151∙4951∙53401
Carmichael numbers: 157∙313∙1093, 157∙937∙6397, 157∙1093∙15601, 157∙2017∙28789, 157∙4993∙11701, 157∙26053∙409033
Carmichael numbers: 163∙379∙2377, 163∙487∙811, 163∙811∙1297, 163∙1297∙42283, 163∙1621∙37747
Carmichael numbers: 167∙4483∙34031, 167∙29383∙490697
Carmichael numbers: 173∙1291∙31907, 173∙10321∙255077, 173∙36809∙155317
Carmichael numbers: 179∙1069∙4451, 179∙3739∙7121, 179∙9257∙57139, 179∙10859∙485941
Carmichael numbers: 181∙271∙9811, 181∙541∙3061, 181∙631∙811, 181∙733∙66337, 181∙1693∙43777, 181∙2953∙3637, 181∙3061∙9721, 181∙5881∙9421, 181∙11161∙15661, 181∙16561∙999181
Carmichael numbers: 191∙421∙431, 191∙571∙15581, 191∙1901∙7411, 191∙3877∙56963, 191∙12541∙342191
Carmichael numbers: 193∙257∙1601, 193∙401∙11057, 193∙577∙5569, 193∙1249∙2593, 193∙2689∙30529, 193∙7681∙211777, 193∙61057∙94273
Carmichael numbers: 199∙397∙4159, 199∙859∙2311, 199∙937∙20719, 199∙991∙32869, 199∙4159∙8713, 199∙8713∙82567
Carmichael numbers: 211∙281∙491, 211∙421∙631, 211∙631∙66571, 211∙1051∙9241, 211∙1741∙4651, 211∙1831∙4111, 211∙2311∙54181, 211∙2521∙3571, 211∙3221∙35771, 211∙3571∙9661, 211∙4019∙11159, 211∙4201∙98491, 211∙32341∙70351, 211∙68041∙127051
Carmichael numbers: 223∙1777∙23311, 223∙2221∙5107, 223∙5107∙37963, 223∙14653∙79699, 223∙25087∙1864801
Carmichael numbers: 227∙1583∙6781, 227∙2713∙5651, 227∙7459∙423299, 227∙21019∙91757
Carmichael numbers: 229∙457∙2053, 229∙571∙4219, 229∙1597∙182857, 229∙2243∙73379, 229∙7069∙32377
Carmichael numbers: 233∙5569∙185369
Carmichael numbers: 239∙409∙3911, 239∙1429∙1667, 239∙1667∙6427, 239∙32369∙234431
Carmichael numbers: 241∙337∙4513, 241∙433∙52177, 241∙1201∙2161, 241∙1361∙4001, 241∙2161∙3361, 241∙3361∙32401, 241∙5521∙110881, 241∙6481∙780961, 241∙7321∙588121, 241∙84961∙181201
Carmichael numbers: 251∙751∙3251, 251∙2251∙56501, 251∙3251∙4001, 251∙4751∙22501, 251∙16001∙803251, 251∙22501∙297251, 251∙31751∙2656501
Carmichael numbers: 257∙641∙1153, 257∙769∙49409, 257∙67073∙3447553, 257∙78593∙403969
Carmichael numbers: 263∙787∙2621, 263∙1049∙3407, 263∙6551∙12577, 263∙71527∙1881161
Carmichael numbers: 269∙1877∙126229, 269∙4289∙384581, 269∙10453∙65393, 269∙15277∙21977
Carmichael numbers: 271∙541∙811, 271∙811∙2971, 271∙1171∙7741, 271∙1801∙16831, 271∙2161∙65071, 271∙4591∙4861, 271∙4861∙77491, 271∙8191∙1109881, 271∙8641∙47791, 271∙9631∙52201, 271∙10531∙1426951, 271∙14797∙1336663
Carmichael numbers: 277∙829∙7177, 277∙1381∙1933, 277∙3313∙9661, 277∙6073∙31741, 277∙18493∙88321, 277∙19597∙36433
Carmichael numbers: 281∙421∙701, 281∙617∙673, 281∙1009∙4649, 281∙1321∙23201, 281∙4201∙9521, 281∙7121∙26681, 281∙9521∙13721, 281∙25621∙84701
Carmichael numbers: 283∙4231∙598687, 283∙17203∙58657
Carmichael numbers: 293∙877∙4673, 293∙1607∙31391, 293∙3943∙5987
Carmichael numbers: 307∙613∙919, 307∙919∙141067, 307∙1531∙3673, 307∙2143∙13159, 307∙3673∙225523, 307∙6427∙246637, 307∙17443∙153001, 307∙18973∙1941571
Carmichael numbers: 311∙1117∙26723, 311∙1303∙2357, 311∙2791∙21701, 311∙3659∙7069, 311∙23251∙33791, 311∙26041∙323951, 311∙28211∙165541, 311∙44641∙52391
Carmichael numbers: 313∙521∙23297, 313∙937∙58657, 313∙1093∙6709, 313∙1249∙55849, 313∙3433∙38377, 313∙3793∙395737, 313∙5449∙12097, 313∙6577∙8761, 313∙7177∙70201, 313∙9049∙472057, 313∙12637∙359581, 313∙49297∙5143321, 313∙51481∙947857, 313∙66457∙184081, 313∙129169∙400297
Carmichael numbers: 317∙18013∙41081, 317∙104281∙2542853
Carmichael numbers: 331∙661∙991, 331∙947∙24113, 331∙991∙4621, 331∙1321∙17491, 331∙2311∙12541, 331∙2971∙49171, 331∙3331∙551281, 331∙4051∙18121, 331∙4621∙14851, 331∙37181∙1758131, 331∙37951∙897271, 331∙41141∙316691
Carmichael numbers: 337∙421∙47293, 337∙449∙21617, 337∙673∙1009, 337∙953∙8681, 337∙1009∙3697, 337∙1597∙12517, 337∙2473∙11113, 337∙3697∙12097, 337∙16369∙1379089, 337∙19489∙597073, 337∙35393∙40433, 337∙58129∙2176609
Carmichael numbers: 347∙3461∙92383, 347∙4153∙29411
Carmichael numbers: 349∙929∙7541, 349∙1741∙2089, 349∙3191∙12239, 349∙4177∙20533, 349∙122149∙21315001
Carmichael numbers: 353∙617∙19801, 353∙1153∙5153, 353∙1321∙66617, 353∙13217∙77761, 353∙130241∙2704417
Carmichael numbers: 359∙43319∙3887881, 359∙46183∙592133
Carmichael numbers: 367∙733∙1831, 367∙1831∙9883, 367∙5003∙42701, 367∙9151∙419803, 367∙24889∙51607, 367∙28183∙574621
Carmichael numbers: 373∙1117∙1861, 373∙1613∙150413, 373∙5581∙1040857, 373∙16741∙81097, 373∙139501∙26016937
Carmichael numbers: 379∙631∙9199, 379∙757∙4159, 379∙2269∙24571, 379∙2539∙21871, 379∙6427∙202987, 379∙9829∙17011, 379∙10639∙268813
Carmichael numbers: 383∙33617∙40111, 383∙38201∙860647, 383∙74873∙3186263
Carmichael numbers: 389∙3299∙6791
Carmichael numbers: 397∙1783∙4951, 397∙2971∙51283, 397∙4357∙8317, 397∙30097∙56629, 397∙55837∙852589, 397∙79201∙10480933, 397∙99793∙370261
Carmichael numbers: 401∙641∙2161, 401∙1201∙1601, 401∙2161∙216641, 401∙2801∙9601, 401∙9521∙19681, 401∙9601∙70001, 401∙15601∙18401, 401∙18401∙567601, 401∙161201∙32320801
Carmichael numbers: 409∙2857∙6529, 409∙6121∙96289, 409∙6529∙22441, 409∙7039∙575791, 409∙35089∙683401, 409∙36721∙114649
Carmichael numbers: 419∙15467∙47653, 419∙22573∙78167, 419∙47653∙539639
Carmichael numbers: 421∙631∙11551, 421∙701∙2381, 421∙3851∙85331, 421∙7561∙289381, 421∙9661∙15121, 421∙13441∙209581, 421∙18481∙39901, 421∙20231∙54251, 421∙35533∙7479697, 421∙42589∙208489, 421∙89041∙12495421
Carmichael numbers: 431∙1721∙29671, 431∙1979∙142159, 431∙8171∙55901, 431∙13331∙168991
Carmichael numbers: 433∙937∙11593, 433∙1297∙2161, 433∙2161∙16417, 433∙2593∙48817, 433∙2953∙21673, 433∙3457∙6481, 433∙3697∙55201, 433∙6481∙87697
Carmichael numbers: 439∙3067∙673207, 439∙3943∙45553, 439∙9199∙2019181, 439∙10513∙17959, 439∙64679∙7098521, 439∙96799∙14164921
Carmichael numbers: 443∙1327∙4421, 443∙2029∙4967, 443∙74257∙143651, 443∙102103∙2380613, 443∙167077∙236471, 443∙251057∙889747
Carmichael numbers: 449∙2689∙3137, 449∙50849∙4566241, 449∙145601∙325249, 449∙202049∙45360001
Carmichael numbers: 457∙3877∙93253, 457∙5701∙8893, 457∙7297∙32377, 457∙15733∙19381, 457∙21433∙163249, 457∙28729∙55633, 457∙71593∙2337001, 457∙73721∙1203233, 457∙114001∙1211593
Carmichael numbers: 461∙691∙1151, 461∙1013∙38917, 461∙1381∙159161, 461∙3541∙23321, 461∙5981∙24841, 461∙26681∙4099981
Carmichael numbers: 463∙2927∙15401, 463∙6007∙39733, 463∙214831∙49733377, 463∙218527∙10117801
Carmichael numbers: 467∙141199∙474389
Carmichael numbers: 479∙57839∙219881
Carmichael numbers: 487∙1459∙8263, 487∙1531∙2683, 487∙1621∙1783, 487∙1783∙108541, 487∙8263∙9721, 487∙12637∙32563, 487∙17011∙2761453, 487∙26731∙110323, 487∙51517∙69499
Carmichael numbers: 491∙1471∙10781, 491∙6959∙569479, 491∙16661∙154351, 491∙41651∙46061, 491∙122501∙6683111, 491∙386611∙637001
Carmichael numbers: 499∙997∙4483, 499∙10459∙39841
Carmichael numbers: 503∙5021∙21587
Carmichael numbers: 509∙3557∙41149, 509∙7621∙23369, 509∙11939∙110491, 509∙86869∙11054081
Carmichael numbers: 521∙1301∙8581, 521∙21841∙41081
Carmichael numbers: 523∙1567∙163909, 523∙6091∙1592797, 523∙9397∙140419, 523∙15661∙481807, 523∙38629∙69427, 523∙155557∙1114471, 523∙193663∙462493
Carmichael numbers: 541∙811∙3511, 541∙1621∙7561, 541∙6661∙257401, 541∙7561∙54541, 541∙12421∙197641, 541∙16561∙814501
Carmichael numbers: 547∙1093∙2731, 547∙2731∙6553, 547∙6553∙35491, 547∙7333∙235951, 547∙26209∙186187, 547∙52963∙827737, 547∙158341∙2624623
Carmichael numbers: 557∙1669∙42257, 557∙38921∙7226333
Carmichael numbers: 563∙28663∙329333
Carmichael numbers: 569∙2273∙117577, 569∙13633∙1108169, 569∙17609∙25561, 569∙21017∙37489, 569∙22153∙787817
Carmichael numbers: 571∙661∙16411, 571∙2281∙2851, 571∙2851∙13681, 571∙6841∙43891, 571∙13681∙1562371, 571∙65323∙18649717
Carmichael numbers: 577∙757∙39709, 577∙1153∙6337, 577∙5569∙100417, 577∙6337∙26497, 577∙20161∙646273, 577∙32833∙37441, 577∙53857∙181729, 577∙79777∙86689, 577∙339841∙15083713, 577∙559297∙819073
Carmichael numbers: 587∙5861∙33403, 587∙9377∙54499, 587∙12893∙36919, 587∙49811∙3654883
Carmichael numbers: 593∙21017∙31081, 593∙35521∙3009137, 593∙176417∙34871761
Carmichael numbers: 599∙2393∙84319, 599∙120199∙17999801, 599∙179999∙35939801, 599∙266111∙547769, 599∙368369∙12979591
Carmichael numbers: 601∙1201∙1801, 601∙1801∙541201, 601∙3001∙200401, 601∙3121∙38281, 601∙3301∙5101, 601∙4201∙4801, 601∙4801∙412201, 601∙5101∙278701, 601∙6151∙7951, 601∙9001∙386401, 601∙19801∙28201, 601∙52201∙3921601, 601∙99901∙923701
Carmichael numbers: 607∙1213∙9091, 607∙4243∙1287751, 607∙21817∙322999, 607∙24847∙1885267, 607∙61813∙7504099, 607∙186649∙12588439, 607∙370873∙45023983, 607∙373903∙22695913
Carmichael numbers: 613∙919∙2143, 613∙1021∙312937, 613∙1327∙73951, 613∙1429∙23053, 613∙2857∙17341, 613∙7549∙87313, 613∙9181∙2813977, 613∙12241∙111997, 613∙51817∙213181, 613∙246637∙783361, 613∙364753∙386173
Carmichael numbers: 617∙661∙1013, 617∙8009∙705937, 617∙16633∙120737, 617∙29569∙2606297, 617∙59753∙81929, 617∙73613∙133981, 617∙129361∙6139673, 617∙137369∙1629937, 617∙383153∙47281081
Carmichael numbers: 619∙1237∙4327, 619∙2267∙26987, 619∙5563∙1721749, 619∙28429∙703903, 619∙53149∙56239, 619∙92083∙452377, 619∙398611∙9490009
Carmichael numbers: 631∙1471∙46411, 631∙5881∙90511, 631∙26209∙82279, 631∙32831∙67481
Carmichael numbers: 641∙4481∙7681, 641∙12161∙26881, 641∙17921∙370561, 641∙19841∙176641
Carmichael numbers: 643∙107857∙2391451
Carmichael numbers: 647∙4523∙19381, 647∙64601∙75583, 647∙188633∙532951, 647∙444449∙7013623
Carmichael numbers: 653∙13367∙2909551, 653∙176041∙732197
Carmichael numbers: 659∙2633∙5923, 659∙23689∙624443, 659∙27919∙34781, 659∙30269∙92779, 659∙73039∙6876101, 659∙92779∙1329161
Carmichael numbers: 661∙991∙131011, 661∙1321∙4621, 661∙2131∙4231, 661∙3191∙6491, 661∙3301∙12541, 661∙4621∙763621, 661∙5281∙81181, 661∙22111∙1623931, 661∙22441∙95701, 661∙138821∙152681
Carmichael numbers: 673∙1009∙14449, 673∙2017∙3361, 673∙3361∙12097, 673∙13441∙1292257, 673∙40801∙155137, 673∙231841∙9178177
Carmichael numbers: 677∙2029∙85853, 677∙4733∙1602121, 677∙6761∙25013, 677∙45293∙511057
Carmichael numbers: 683∙8867∙16369, 683∙11161∙206027, 683∙15749∙32303, 683∙42967∙2934647, 683∙94117∙9183131
Carmichael numbers: 691∙7591∙2622691, 691∙16561∙2288731, 691∙31051∙71761, 691∙34501∙2648911, 691∙69691∙3009781, 691∙743131∙1330321
Carmichael numbers: 701∙2801∙10501, 701∙3701∙1297201, 701∙3851∙899851, 701∙6301∙7001, 701∙18401∙58901, 701∙41651∙2245951, 701∙44101∙170801, 701∙46901∙319201, 701∙52501∙296801, 701∙53201∙632101
Carmichael numbers: 709∙4957∙12037, 709∙7789∙16993, 709∙9677∙21713, 709∙36109∙5120257, 709∙210277∙819157
Carmichael numbers: 719∙97649∙190271
Carmichael numbers: 727∙1453∙2179, 727∙2179∙792067, 727∙2663∙193601, 727∙3631∙8713, 727∙4423∙321553, 727∙176903∙32152121, 727∙308551∙1823713, 727∙651223∙2784937
Carmichael numbers: 733∙5857∙84181, 733∙13177∙47581, 733∙18301∙789097, 733∙22571∙2363507, 733∙25621∙9390097, 733∙150427∙1238911, 733∙271573∙22118113, 733∙631717∙3561913
Carmichael numbers: 739∙821∙4019, 739∙3691∙454609, 739∙10333∙2545363, 739∙62731∙1783009, 739∙152029∙1321759
Carmichael numbers: 743∙6679∙225569, 743∙6997∙9011, 743∙596569∙7266407
Carmichael numbers: 751∙2251∙10501, 751∙2851∙237901, 751∙21751∙181501, 751∙109751∙649001, 751∙123001∙1338751, 751∙153001∙1767751, 751∙191251∙10259251, 751∙318751∙2418001
Carmichael numbers: 757∙2017∙18397, 757∙2269∙858817, 757∙15121∙3815533, 757∙27541∙79273, 757∙32257∙2219869, 757∙33013∙59221, 757∙184843∙633151, 757∙627481∙6506893
Carmichael numbers: 761∙2129∙31769, 761∙2281∙3041, 761∙3041∙771401, 761∙6841∙19001, 761∙8969∙1137569, 761∙13681∙101081, 761∙19001∙1032841, 761∙41801∙497041, 761∙230281∙1184081, 761∙251941∙339341, 761∙314641∙497801
Carmichael numbers: 769∙6529∙9601, 769∙41729∙697601
Carmichael numbers: 773∙22003∙122363, 773∙44777∙47093
Carmichael numbers: 787∙3931∙9433, 787∙5503∙45589, 787∙106373∙3348623
Carmichael numbers: 797∙2389∙476009, 797∙3583∙16319, 797∙5573∙11941, 797∙21493∙428249, 797∙58109∙7718813, 797∙148853∙859681
Carmichael numbers: 809∙5657∙9697, 809∙78781∙176549, 809∙82013∙22116173, 809∙176549∙2197357, 809∙453289∙1171601
Carmichael numbers: 811∙1621∙438211, 811∙4051∙19441, 811∙4591∙744661, 811∙6481∙17011, 811∙19441∙3153331, 811∙77761∙1189891, 811∙86131∙478441
Carmichael numbers: 821∙1231∙6971, 821∙15581∙42641, 821∙137597∙6275953
Carmichael numbers: 823∙2467∙4111, 823∙4111∙23017, 823∙4933∙9043, 823∙27127∙637873, 823∙341953∙31269703
Carmichael numbers: 827∙2243∙2833, 827∙4957∙5783, 827∙24781∙476603, 827∙101009∙2880499, 827∙691363∙57175721
Carmichael numbers: 829∙1657∙17389, 829∙9109∙15733, 829∙10949∙2269181, 829∙24841∙1872109, 829∙140761∙5556709
Carmichael numbers: 839∙5867∙223747
Carmichael numbers: 853∙2557∙4261, 853∙7669∙594697, 853∙12781∙5451097, 853∙17041∙309277, 853∙19597∙185737
Carmichael numbers: 857∙6421∙127973, 857∙10273∙160073, 857∙95873∙115561, 857∙796937∙9229393
Carmichael numbers: 859∙2861∙3719, 859∙8581∙9439, 859∙9439∙150151, 859∙27457∙66067, 859∙321751∙1039039
Carmichael numbers: 863∙24137∙38791, 863∙28447∙153437, 863∙38791∙62927, 863∙56893∙68099
Carmichael numbers: 877∙1753∙56941, 877∙3067∙30223, 877∙6133∙8761, 877∙24091∙7042603, 877∙36793∙6453493, 877∙263677∙8894029
Carmichael numbers: 881∙2861∙840181, 881∙22441∙57641, 881∙130241∙16391761
Carmichael numbers: 883∙2647∙44101, 883∙8191∙267877, 883∙11467∙35281, 883∙15877∙824671, 883∙16633∙358219, 883∙21757∙3842287, 883∙30871∙134947, 883∙42337∙216091, 883∙126127∙161407, 883∙260191∙114874327, 883∙403957∙10808911, 883∙507151∙531847
Carmichael numbers: 887∙14177∙50503
Carmichael numbers: 907∙7853∙16007, 907∙137713∙24981139
Carmichael numbers: 911∙2003∙912367, 911∙9283∙1208117, 911∙9311∙55441, 911∙11831∙898171, 911∙16381∙28211, 911∙30941∙4026751, 911∙55511∙12642631, 911∙167441∙204751, 911∙175631∙2962961, 911∙185641∙1551551, 911∙227501∙2328691
Carmichael numbers: 919∙8263∙949213, 919∙15607∙170749, 919∙60589∙11136259, 919∙129439∙569161, 919∙156979∙321301, 919∙311203∙2918323, 919∙877609∙21797911
Carmichael numbers: 929∙5569∙23201, 929∙6961∙35729, 929∙42689∙1071841, 929∙139201∙307169
Carmichael numbers: 937∙1873∙70201, 937∙6553∙7489, 937∙7489∙1002457, 937∙21529∙3362113, 937∙38377∙5993209, 937∙177841∙820873
Carmichael numbers: 941∙5171∙23971, 941∙6581∙8461, 941∙8461∙361901, 941∙28201∙102461, 941∙44651∙4668511, 941∙209621∙1133641, 941∙322891∙701711, 941∙355321∙1732421
Carmichael numbers: 947∙29327∙1983763, 947∙47129∙299539, 947∙307451∙10398433
Carmichael numbers: 953∙2857∙9521, 953∙5881∙18257, 953∙17137∙69497, 953∙52361∙159937, 953∙159937∙2771273
Carmichael numbers: 967∙1289∙25439, 967∙1933∙4831, 967∙4831∙11593, 967∙26083∙5044453, 967∙62791∙7589863, 967∙88873∙1909783, 967∙156493∙30265747
Carmichael numbers: 971∙3881∙753691, 971∙8731∙44621, 971∙12611∙3061321, 971∙110581∙635351, 971∙142591∙2387171, 971∙169751∙648931, 971∙1324051∙3263081
Carmichael numbers: 977∙2441∙794953, 977∙5857∙12689, 977∙6833∙39041, 977∙17569∙41969, 977∙478241∙155747153
Carmichael numbers: 983∙3929∙8839, 983∙8839∙1241249, 983∙970217∙190744663
Carmichael numbers: 991∙4951∙58411, 991∙10111∙501001, 991∙16831∙26731, 991∙56431∙607861, 991∙99991∙5215321, 991∙118801∙206911, 991∙138403∙336997, 991∙167311∙312841, 991∙338581∙890011, 991∙658351∙1924561
Carmichael numbers: 997∙1993∙56773, 997∙8467∙367027, 997∙12451∙4137883, 997∙17929∙130477, 997∙29383∙450691, 997∙167329∙15166093, 997∙1002973∙99996409
──────── 1038 Carmichael numbers found.
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