Carmichael 3 strong pseudoprimes: Difference between revisions
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<pre>
──────── 8716 Carmichael numbers found.
</pre>
=={{header|Ring}}==
<lang ring>
# Project : Carmichael 3 strong pseudoprimes
# Date : 2017/11/29
# Author : Gal Zsolt (~ CalmoSoft ~)
# Email : <calmosoft@gmail.com>
see "The following are Carmichael munbers for p1 <= 61:" + nl
see "p1 p2 p3 product" + nl
for p = 2 to 61
carmichael3(p)
next
func carmichael3(p1)
if isprime(p1) = 0 return ok
for h3 = 1 to p1 -1
t1 = (h3 + p1) * (p1 -1)
t2 = (-p1 * p1) % h3
if t2 < 0
t2 = t2 + h3
ok
for d = 1 to h3 + p1 -1
if t1 % d = 0 and t2 = (d % h3)
p2 = 1 + (t1 / d)
if isprime(p2) = 0
loop
ok
p3 = 1 + floor((p1 * p2 / h3))
if isprime(p3) = 0 or ((p2 * p3) % (p1 -1)) != 1
loop
ok
see "" + p1 + " " + p2 + " " + p3 + " " + p1*p2*p3 + nl
ok
next
next
func isprime(num)
if (num <= 1) return 0 ok
if (num % 2 = 0) and num != 2
return 0
ok
for i = 3 to floor(num / 2) -1 step 2
if (num % i = 0)
return 0
ok
next
return 1
</lang>
Output:
<pre>
The following are Carmichael munbers for p1 <= 61:
p1 p2 p3 product
== == == =======
3 11 17 561
5 29 73 10585
5 17 29 2465
5 13 17 1105
7 19 67 8911
7 31 73 15841
7 13 31 2821
7 23 41 6601
7 73 103 52633
7 13 19 1729
13 61 397 314821
13 37 241 115921
13 97 421 530881
13 37 97 46657
13 37 61 29341
17 41 233 162401
17 353 1201 7207201
19 43 409 334153
19 199 271 1024651
23 199 353 1615681
29 113 1093 3581761
29 197 953 5444489
31 991 15361 471905281
31 61 631 1193221
31 151 1171 5481451
31 61 271 512461
31 61 211 399001
31 271 601 5049001
31 181 331 1857241
37 109 2017 8134561
37 73 541 1461241
37 613 1621 36765901
37 73 181 488881
37 73 109 294409
41 1721 35281 2489462641
41 881 12041 434932961
41 101 461 1909001
41 241 761 7519441
41 241 521 5148001
41 73 137 410041
41 61 101 252601
43 631 13567 368113411
43 271 5827 67902031
43 127 2731 14913991
43 127 1093 5968873
43 211 757 6868261
43 631 1597 43331401
43 127 211 1152271
43 211 337 3057601
43 433 643 11972017
43 547 673 15829633
43 3361 3907 564651361
47 3359 6073 958762729
47 1151 1933 104569501
47 3727 5153 902645857
53 157 2081 17316001
53 79 599 2508013
53 157 521 4335241
59 1451 2089 178837201
61 421 12841 329769721
61 181 5521 60957361
61 1301 19841 1574601601
61 277 2113 35703361
61 181 1381 15247621
61 541 3001 99036001
61 661 2521 101649241
61 271 571 9439201
61 241 421 6189121
61 3361 4021 824389441
</pre>
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