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Old 2019-08-11, 05:01   #1
devarajkandadai
 
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Default Continued product Carmichael numbers

Let me give an example of a set of continued product Carmichael numbers:
a)2465 = 5*17*29 b)278545 = 5*17*29*113 c)93969665=5*17*29*113*337 d)63174284545 = 5*17*29*113*337*673 and e)169875651141505 = 5*17*29*113*337*673*2689

Algorithm for this type of c.p.Carmichael numbers is simple and I will illustrate
how to derive b) above starting from a). Largest prime factor of a) is 29. Check the first prime generated by 28*k + 1; when k = 4 we get 113.
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Old 2019-08-13, 04:43   #2
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Quote:
Originally Posted by devarajkandadai View Post
Let me give an example of a set of continued product Carmichael numbers:
a)2465 = 5*17*29 b)278545 = 5*17*29*113 c)93969665=5*17*29*113*337 d)63174284545 = 5*17*29*113*337*673 and e)169875651141505 = 5*17*29*113*337*673*2689

Algorithm for this type of c.p.Carmichael numbers is simple and I will illustrate
how to derive b) above starting from a). Largest prime factor of a) is 29. Check the first prime generated by 28*k + 1; when k = 4 we get 113.
Another set of continued product Carmichael numbers ( prefer to call them "spiral Carmichael numbers"): a)2821 = 7*13* 31
b)172081= 7*13*31*61
c)31146661 = 7*13*31*61*181
d)16850343601= 7*13*31*61*181*541
Important point: possibility of constructing such spiral Carmichael numbers strengthens my conjecture that, r, the number of prime factors of a Carmichael number is not bounded.

Last fiddled with by devarajkandadai on 2019-08-13 at 04:50
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Old 2019-09-24, 03:14   #3
devarajkandadai
 
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Quote:
Originally Posted by devarajkandadai View Post
Another set of continued product Carmichael numbers ( prefer to call them "spiral Carmichael numbers"): a)2821 = 7*13* 31
b)172081= 7*13*31*61
c)31146661 = 7*13*31*61*181
d)16850343601= 7*13*31*61*181*541
Important point: possibility of constructing such spiral Carmichael numbers strengthens my conjecture that, r, the number of prime factors of a Carmichael number is not bounded.
Another set of spiral Carmichael numbers: 252601 = 41*61*101
151813201 = 41*61*101*601
182327654401=41*61*101*601*1201
875355068779201 = 41*61*101*601*1201*4801*
12605988345489273601 = 41*61*101*601*1201*4801*14401
726117534688527648691201 = 41*61*101*601*1201*4801*14401*57601
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