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2021-07-11, 19:07   #12
enzocreti

Mar 2018

10238 Posts
...

Quote:
 Originally Posted by rudy235 I never quite understand what you are trying to say. Can you explain to the unwashed masses the function pg? What is it? Paying guest? Picogram?
the last you said

 2022-01-03, 13:06 #14 enzocreti   Mar 2018 21316 Posts 92233=427x6^3+1 92233=6^3=51456 mod 427 ((92233-51456)-1)/3-12592=10^3 12592 divides 541456 PG(51456) and PG(541456) are primes 92233-51456=1=69660 mod 1699 13592=1699*8 43*(((51456+(3^6-1)*4)/4)-10^3)=541456 69660-(487-51456)=69660-(92233-51456)=0 mod (71x1699) (69660-487)=0 mod 313 (69660-486)=0 mod 427 486=162x3 162 divides 69660 -449449-13=64=541456+13 mod 139 so 541456=51 mod 139 (449x13=-1 mod 139) 92020=541456+13-449449 331259=71*6^6=259 mod 331 331259=44 mod 71 331249-44=331215 that Is the concatenation of 331 and 215 331259-44-215 Is a multiple of 331 44+215=259 71x6^6-331259+92020=6^2-6^5 mod 311 (6^2-6^5)=7740 which divides 69660 (7740=1 mod 71) multyplying by 9 both sides 71x6^6x9-331259x9+92020x9=-69660 mod 311 331215 is the concatenation of 331 and 215 331+215=546 546 divides 75894 and 56238 pg(75894) and pg(56238) are primes 75894-92020/2=215x139-1 546=215+331 215x139 can be cancelled in both sides this leaves 46009-46010=-1 56238 can be factorized as (139-6^2)*(331+215)=56238 probably there is something in 79*3^j pg(79) is prime by the way 79*3^2=711 and 69660=71x711+2131x3^2 79*3^3=2131+1 71x79+2131=7740 which divides 69660 79x3^2=1 mod 71 69660-19179=71x79x3^2 239239=-9 mod 12592 541456=239239+9 mod 12592 92020=3867+9 mod 12592 23004*46009-1-(92020-6)=3539x13x23003 i think that there should be some group in action... pg(75894) and pg(56238) are primes with 75894 and 56238 multiple of 139 75894+56238=132132=1 mod (1861x71) 331259=1 mod 1861 75894+56238=331259 mod (1861x107) 331259-132132=107x1861 75894+56238-1=71x1861 107=71+6^2 56238 and 75894 are congruent to +/- 6 mod 132 in particular (75894+6)/132+1=24^2 so 331259=56238+75894+92020+107x1001 Last fiddled with by enzocreti on 2022-01-17 at 09:32

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