Carmichael 3 strong pseudoprimes: Difference between revisions

===slightly optimized===

</pre>

===more optimized===

This REXX version (pre-)generates a number of primes to assist the &nbsp; '''isPrime''' &nbsp; function.

<lang rexx>/*REXX program calculates Carmichael 3─strong pseudoprimes (up to and including N). */

numeric digits 18 /*handle big dig #s (9 is the default).*/

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*/

#=0; @.=0 /*number of Carmichael numbers so far. */

@.2=1; @.3=1; @.5=1; @.7=1; @.11=1; @.13=1; @.17=1; @.19=1; @.23=1; @.29=1; @.31=1; @.37=1

HP=37; do i=HP+2 by 2 for N*20; if isPrime(i) then do; @.i=1; HP=i; end; end /*i*/

HP=HP+2

/*[↑] prime number memoization array. */

do p=3 to N by 2; pm=p-1; bot=0; top=0 /*step through some (odd) prime numbers*/

if \isPrime(p) then iterate; nps=-p*p /*is P a prime? No, then skip it.*/

!.=0 /*the list of Carmichael #'s (so far).*/

do h3=2 to pm; g=h3+p /*find Carmichael #s for this prime. */

gPM=g*pm; npsH3=((nps//h3)+h3)//h3 /*define a couple of shortcuts for pgm.*/

/* [↓] perform some weeding of D values*/

do d=1 for g-1; if gPM//d \== 0 then iterate

if npsH3 \== d//h3 then iterate

q=1+gPM%d; if \isPrime(q) then iterate

r=1+p*q%h3; if q*r//pm\==1 then iterate

if \isPrime(r) then iterate

#=#+1; !.q=r /*bump Carmichael counter; add to array*/

if bot==0 then bot=q; bot=min(bot,q); top=max(top,q)

end /*d*/

end /*h3*/

$= /*display a list of some Carmichael #s.*/

do j=bot to top by 2 while tell; if !.j\==0 then $=$ p"∙"j'∙'!.j

end /*j*/

if $\=='' then say 'Carmichael number: ' strip($)

end /*p*/

say

say '──────── ' # " Carmichael numbers found."

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<HP then return 0; if x//2==0 then return 0; if x// 3==0 then return 0

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//29==0 then return 0

if x//31==0 then return 0; if x//37==0 then return 0

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''' &nbsp; when the following us used for input: &nbsp; <tt> 1000 </tt>

<pre style="height:72ex">

Carmichael number: 3∙11∙17

Carmichael number: 5∙13∙17 5∙17∙29 5∙29∙73

Carmichael number: 7∙13∙19 7∙19∙67 7∙23∙41 7∙31∙73 7∙73∙103

Carmichael number: 13∙37∙61 13∙61∙397 13∙97∙421

Carmichael number: 17∙41∙233 17∙353∙1201

Carmichael number: 19∙43∙409 19∙199∙271

Carmichael number: 23∙199∙353

Carmichael number: 29∙113∙1093 29∙197∙953

Carmichael number: 31∙61∙211 31∙151∙1171 31∙181∙331 31∙271∙601 31∙991∙15361

Carmichael number: 37∙73∙109 37∙109∙2017 37∙613∙1621

Carmichael number: 41∙61∙101 41∙73∙137 41∙101∙461 41∙241∙521 41∙881∙12041 41∙1721∙35281

Carmichael number: 43∙127∙211 43∙211∙337 43∙271∙5827 43∙433∙643 43∙547∙673 43∙631∙1597 43∙3361∙3907

Carmichael number: 47∙1151∙1933 47∙3359∙6073 47∙3727∙5153

Carmichael number: 53∙79∙599 53∙157∙521

Carmichael number: 59∙1451∙2089

Carmichael number: 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 number: 67∙331∙463 67∙2311∙51613

Carmichael number: 71∙271∙521 71∙421∙491 71∙631∙701 71∙701∙5531 71∙911∙9241

Carmichael number: 73∙157∙2293 73∙379∙523 73∙601∙21937 73∙937∙13681

Carmichael number: 79∙2237∙25247

Carmichael number: 83∙2953∙4019 83∙6971∙289297

Carmichael number: 89∙353∙617 89∙617∙3433 89∙881∙7129 89∙4049∙120121

Carmichael number: 97∙193∙1249 97∙673∙769 97∙769∙10657 97∙1201∙38833 97∙2113∙5857

Carmichael number: 101∙151∙251 101∙1301∙43801

Carmichael number: 103∙647∙1361 103∙1123∙6427 103∙3571∙183907 103∙3877∙4591 103∙5407∙185641

Carmichael number: 107∙743∙1061 107∙3181∙26183

Carmichael number: 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 number: 113∙337∙449 113∙827∙18691 113∙6833∙85793 113∙8737∙22961

Carmichael number: 127∙631∙26713 127∙659∙1373 127∙991∙3313 127∙2143∙30241 127∙16633∙422479

Carmichael number: 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 number: 137∙409∙14009 137∙953∙5441 137∙3673∙20129 137∙5441∙11833

Carmichael number: 139∙691∙829 139∙3359∙66701 139∙4003∙92737 139∙4969∙8971 139∙17389∙21391

Carmichael number: 149∙593∙29453 149∙1481∙3109

Carmichael number: 151∙211∙541 151∙331∙3571 151∙601∙751 151∙701∙1451 151∙751∙8101 151∙2551∙192601 151∙4951∙53401

Carmichael number: 157∙313∙1093 157∙937∙6397 157∙1093∙15601 157∙2017∙28789 157∙4993∙11701 157∙26053∙409033

Carmichael number: 163∙379∙2377 163∙487∙811 163∙811∙1297 163∙1297∙42283 163∙1621∙37747

Carmichael number: 167∙4483∙34031 167∙29383∙490697

Carmichael number: 173∙1291∙31907 173∙10321∙255077 173∙36809∙155317

Carmichael number: 179∙1069∙4451 179∙3739∙7121 179∙9257∙57139 179∙10859∙485941

Carmichael number: 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 number: 191∙421∙431 191∙571∙15581 191∙1901∙7411 191∙3877∙56963 191∙12541∙342191

Carmichael number: 193∙257∙1601 193∙401∙11057 193∙577∙5569 193∙1249∙2593 193∙2689∙30529 193∙7681∙211777 193∙61057∙94273

Carmichael number: 199∙397∙4159 199∙859∙2311 199∙937∙20719 199∙991∙32869 199∙4159∙8713 199∙8713∙82567

Carmichael number: 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 number: 223∙1777∙23311 223∙2221∙5107 223∙5107∙37963 223∙14653∙79699 223∙25087∙1864801

Carmichael number: 227∙1583∙6781 227∙2713∙5651 227∙7459∙423299 227∙21019∙91757

Carmichael number: 229∙457∙2053 229∙571∙4219 229∙1597∙182857 229∙2243∙73379 229∙7069∙32377

Carmichael number: 233∙5569∙185369

Carmichael number: 239∙409∙3911 239∙1429∙1667 239∙1667∙6427 239∙32369∙234431

Carmichael number: 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 number: 251∙751∙3251 251∙2251∙56501 251∙3251∙4001 251∙4751∙22501 251∙16001∙803251 251∙22501∙297251 251∙31751∙2656501

Carmichael number: 257∙641∙1153 257∙769∙49409 257∙67073∙3447553 257∙78593∙403969

Carmichael number: 263∙787∙2621 263∙1049∙3407 263∙6551∙12577 263∙71527∙1881161

Carmichael number: 269∙1877∙126229 269∙4289∙384581 269∙10453∙65393 269∙15277∙21977

Carmichael number: 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 number: 277∙829∙7177 277∙1381∙1933 277∙3313∙9661 277∙6073∙31741 277∙18493∙88321 277∙19597∙36433

Carmichael number: 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 number: 283∙4231∙598687 283∙17203∙58657

Carmichael number: 293∙877∙4673 293∙1607∙31391 293∙3943∙5987

Carmichael number: 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 number: 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 number: 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 number: 317∙18013∙41081 317∙104281∙2542853

Carmichael number: 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 number: 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 number: 347∙3461∙92383 347∙4153∙29411

Carmichael number: 349∙929∙7541 349∙1741∙2089 349∙3191∙12239 349∙4177∙20533 349∙122149∙21315001

Carmichael number: 353∙617∙19801 353∙1153∙5153 353∙1321∙66617 353∙13217∙77761 353∙130241∙2704417

Carmichael number: 359∙43319∙3887881 359∙46183∙592133

Carmichael number: 367∙733∙1831 367∙1831∙9883 367∙5003∙42701 367∙9151∙419803 367∙24889∙51607 367∙28183∙574621

Carmichael number: 373∙1117∙1861 373∙1613∙150413 373∙5581∙1040857 373∙16741∙81097 373∙139501∙26016937

Carmichael number: 379∙631∙9199 379∙757∙4159 379∙2269∙24571 379∙2539∙21871 379∙6427∙202987 379∙9829∙17011 379∙10639∙268813

Carmichael number: 383∙33617∙40111 383∙38201∙860647 383∙74873∙3186263

Carmichael number: 389∙3299∙6791

Carmichael number: 397∙1783∙4951 397∙2971∙51283 397∙4357∙8317 397∙30097∙56629 397∙55837∙852589 397∙79201∙10480933 397∙99793∙370261

Carmichael number: 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 number: 409∙2857∙6529 409∙6121∙96289 409∙6529∙22441 409∙7039∙575791 409∙35089∙683401 409∙36721∙114649

Carmichael number: 419∙15467∙47653 419∙22573∙78167 419∙47653∙539639

Carmichael number: 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 number: 431∙1721∙29671 431∙1979∙142159 431∙8171∙55901 431∙13331∙168991

Carmichael number: 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 number: 439∙3067∙673207 439∙3943∙45553 439∙9199∙2019181 439∙10513∙17959 439∙64679∙7098521 439∙96799∙14164921

Carmichael number: 443∙1327∙4421 443∙2029∙4967 443∙74257∙143651 443∙102103∙2380613 443∙167077∙236471 443∙251057∙889747

Carmichael number: 449∙2689∙3137 449∙50849∙4566241 449∙145601∙325249 449∙202049∙45360001

Carmichael number: 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 number: 461∙691∙1151 461∙1013∙38917 461∙1381∙159161 461∙3541∙23321 461∙5981∙24841 461∙26681∙4099981

Carmichael number: 463∙2927∙15401 463∙6007∙39733 463∙214831∙49733377 463∙218527∙10117801

Carmichael number: 467∙141199∙474389

Carmichael number: 479∙57839∙219881

Carmichael number: 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 number: 491∙1471∙10781 491∙6959∙569479 491∙16661∙154351 491∙41651∙46061 491∙122501∙6683111 491∙386611∙637001

Carmichael number: 499∙997∙4483 499∙10459∙39841

Carmichael number: 503∙5021∙21587

Carmichael number: 509∙3557∙41149 509∙7621∙23369 509∙11939∙110491 509∙86869∙11054081

Carmichael number: 521∙1301∙8581 521∙21841∙41081

Carmichael number: 523∙1567∙163909 523∙6091∙1592797 523∙9397∙140419 523∙15661∙481807 523∙38629∙69427 523∙155557∙1114471 523∙193663∙462493

Carmichael number: 541∙811∙3511 541∙1621∙7561 541∙6661∙257401 541∙7561∙54541 541∙12421∙197641 541∙16561∙814501

Carmichael number: 547∙1093∙2731 547∙2731∙6553 547∙6553∙35491 547∙7333∙235951 547∙26209∙186187 547∙52963∙827737 547∙158341∙2624623

Carmichael number: 557∙1669∙42257 557∙38921∙7226333

Carmichael number: 563∙28663∙329333

Carmichael number: 569∙2273∙117577 569∙13633∙1108169 569∙17609∙25561 569∙21017∙37489 569∙22153∙787817

Carmichael number: 571∙661∙16411 571∙2281∙2851 571∙2851∙13681 571∙6841∙43891 571∙13681∙1562371 571∙65323∙18649717

Carmichael number: 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 number: 587∙5861∙33403 587∙9377∙54499 587∙12893∙36919 587∙49811∙3654883

Carmichael number: 593∙21017∙31081 593∙35521∙3009137 593∙176417∙34871761

Carmichael number: 599∙2393∙84319 599∙120199∙17999801 599∙179999∙35939801 599∙266111∙547769 599∙368369∙12979591

Carmichael number: 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 number: 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 number: 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 number: 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 number: 619∙1237∙4327 619∙2267∙26987 619∙5563∙1721749 619∙28429∙703903 619∙53149∙56239 619∙92083∙452377 619∙398611∙9490009

Carmichael number: 631∙1471∙46411 631∙5881∙90511 631∙26209∙82279 631∙32831∙67481

Carmichael number: 641∙4481∙7681 641∙12161∙26881 641∙17921∙370561 641∙19841∙176641

Carmichael number: 643∙107857∙2391451

Carmichael number: 647∙4523∙19381 647∙64601∙75583 647∙188633∙532951 647∙444449∙7013623

Carmichael number: 653∙13367∙2909551 653∙176041∙732197

Carmichael number: 659∙2633∙5923 659∙23689∙624443 659∙27919∙34781 659∙30269∙92779 659∙73039∙6876101 659∙92779∙1329161

Carmichael number: 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 number: 673∙1009∙14449 673∙2017∙3361 673∙3361∙12097 673∙13441∙1292257 673∙40801∙155137 673∙231841∙9178177

Carmichael number: 677∙2029∙85853 677∙4733∙1602121 677∙6761∙25013 677∙45293∙511057

Carmichael number: 683∙8867∙16369 683∙11161∙206027 683∙15749∙32303 683∙42967∙2934647 683∙94117∙9183131

Carmichael number: 691∙7591∙2622691 691∙16561∙2288731 691∙31051∙71761 691∙34501∙2648911 691∙69691∙3009781 691∙743131∙1330321

Carmichael number: 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 number: 709∙4957∙12037 709∙7789∙16993 709∙9677∙21713 709∙36109∙5120257 709∙210277∙819157

Carmichael number: 719∙97649∙190271

Carmichael number: 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 number: 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 number: 739∙821∙4019 739∙3691∙454609 739∙10333∙2545363 739∙62731∙1783009 739∙152029∙1321759

Carmichael number: 743∙6679∙225569 743∙6997∙9011 743∙596569∙7266407

Carmichael number: 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 number: 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 number: 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 number: 769∙6529∙9601 769∙41729∙697601

Carmichael number: 773∙22003∙122363 773∙44777∙47093

Carmichael number: 787∙3931∙9433 787∙5503∙45589 787∙106373∙3348623

Carmichael number: 797∙2389∙476009 797∙3583∙16319 797∙5573∙11941 797∙21493∙428249 797∙58109∙7718813 797∙148853∙859681

Carmichael number: 809∙5657∙9697 809∙78781∙176549 809∙82013∙22116173 809∙176549∙2197357 809∙453289∙1171601

Carmichael number: 811∙1621∙438211 811∙4051∙19441 811∙4591∙744661 811∙6481∙17011 811∙19441∙3153331 811∙77761∙1189891 811∙86131∙478441

Carmichael number: 821∙1231∙6971 821∙15581∙42641 821∙137597∙6275953

Carmichael number: 823∙2467∙4111 823∙4111∙23017 823∙4933∙9043 823∙27127∙637873 823∙341953∙31269703

Carmichael number: 827∙2243∙2833 827∙4957∙5783 827∙24781∙476603 827∙101009∙2880499 827∙691363∙57175721

Carmichael number: 829∙1657∙17389 829∙9109∙15733 829∙10949∙2269181 829∙24841∙1872109 829∙140761∙5556709

Carmichael number: 839∙5867∙223747

Carmichael number: 853∙2557∙4261 853∙7669∙594697 853∙12781∙5451097 853∙17041∙309277 853∙19597∙185737

Carmichael number: 857∙6421∙127973 857∙10273∙160073 857∙95873∙115561 857∙796937∙9229393

Carmichael number: 859∙2861∙3719 859∙8581∙9439 859∙9439∙150151 859∙27457∙66067 859∙321751∙1039039

Carmichael number: 863∙24137∙38791 863∙28447∙153437 863∙38791∙62927 863∙56893∙68099

Carmichael number: 877∙1753∙56941 877∙3067∙30223 877∙6133∙8761 877∙24091∙7042603 877∙36793∙6453493 877∙263677∙8894029

Carmichael number: 881∙2861∙840181 881∙22441∙57641 881∙130241∙16391761

Carmichael number: 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 number: 887∙14177∙50503

Carmichael number: 907∙7853∙16007 907∙137713∙24981139

Carmichael number: 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 number: 919∙8263∙949213 919∙15607∙170749 919∙60589∙11136259 919∙129439∙569161 919∙156979∙321301 919∙311203∙2918323 919∙877609∙21797911

Carmichael number: 929∙5569∙23201 929∙6961∙35729 929∙42689∙1071841 929∙139201∙307169

Carmichael number: 937∙1873∙70201 937∙6553∙7489 937∙7489∙1002457 937∙21529∙3362113 937∙38377∙5993209 937∙177841∙820873

Carmichael number: 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 number: 947∙29327∙1983763 947∙47129∙299539 947∙307451∙10398433

Carmichael number: 953∙2857∙9521 953∙5881∙18257 953∙17137∙69497 953∙52361∙159937 953∙159937∙2771273

Carmichael number: 967∙1289∙25439 967∙1933∙4831 967∙4831∙11593 967∙26083∙5044453 967∙62791∙7589863 967∙88873∙1909783 967∙156493∙30265747

Carmichael number: 971∙3881∙753691 971∙8731∙44621 971∙12611∙3061321 971∙110581∙635351 971∙142591∙2387171 971∙169751∙648931 971∙1324051∙3263081

Carmichael number: 977∙2441∙794953 977∙5857∙12689 977∙6833∙39041 977∙17569∙41969 977∙478241∙155747153

Carmichael number: 983∙3929∙8839 983∙8839∙1241249 983∙970217∙190744663

Carmichael number: 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 number: 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.