541456 and 51456. I checked 20 numbers 2000 times and found 200 patterns!! - Page 7

enzocreti · 2018-12-17, 08:52

never mind it is easy to proof

any explanation instead for this:
when pg(43k) is prime and k is odd as in the case of pg(215), then 43k is congruent to 7 mod 13.
when pg(43k) is prime and k is even as in the case of pg(69660), then 43k is 6 mod 13.

enzocreti · 2018-12-17, 10:50

pg(215) is congruent to the prime 21015781248582109976561479237247175760828678449588166559266766851 mod (2^214-1)

enzocreti · 2018-12-17, 13:23

are all coincidences?

enzocreti · 2018-12-17, 14:14

pg(51456) and pg(541456) are both primes. If I am right, both the probable primes are of the form 8400s+367.

enzocreti · 2018-12-17, 14:52

the probable primes pg(51456) and pg(541456) end both with digits 55967! by the way 55967 is prime

enzocreti · 2018-12-17, 17:49

as I said it is at least curious that pg(51456) and pg(541456) are both primes and 541456=700^2+51456
moreover 541456 and 51456 are both congruent to 111 mod 35

enzocreti · 2018-12-17, 17:56

moreover (541456-13999)/7=75351
(51456-13999)/7=5351

science_man_88 · 2018-12-17, 18:14

Quote:

Originally Posted by enzocreti

as I said it is at least curious that pg(51456) and pg(541456) are both primes and 541456=700^2+51456
moreover 541456 and 51456 are both congruent to 111 mod 35

All both numbers being 111 mod 35 means, is that their difference is divisible by 35, 490000 = 350000+2*35000+2*3500 so what. since 35 divides into 700 , there's no real mystery other than what makes both pg numbers prime. which if the two values chosen are highly composite numbers or have neighbors that fill in the gaps, then it increases their likelihood to be prime potentially. As the Mersenne numbers concatenated have a lot of factors if their exponents do. So most of the mystique goes away.

enzocreti · 2018-12-17, 18:31

mod(pg(51456),350000)=5967
mod(pg(541456),350000)=255967

enzocreti · 2018-12-17, 19:33

pg(215),pg(69660),pg(92020) and pg(541456) are the probable primes where k is a multiple of 43. Infact:

pg(43*5) is prime
pg(43*1620) is prime
pg(43*2140) is prime
pg(43*12592) is prime

now note that 5 (odd) is congruent to -8 mod 13
1620 (even) is congruent to 8 mod 13
2140 (even) is congruent to 8 mod 13
12592 (even) is congruent to 8 mod 13

enzocreti · 2018-12-17, 20:04

pg(67=67*1) and pg(51456=67*768) are probable primes

1 is congruent to 1 mod 13
768 is congruent to 1 mod 13

2018-12-17, 08:52	#67
enzocreti Mar 2018 1022₈ Posts	never mind never mind it is easy to proof any explanation instead for this: when pg(43k) is prime and k is odd as in the case of pg(215), then 43k is congruent to 7 mod 13. when pg(43k) is prime and k is even as in the case of pg(69660), then 43k is 6 mod 13. Last fiddled with by enzocreti on 2018-12-17 at 11:16 Reason: typo

2018-12-17, 10:50	#68
enzocreti Mar 2018 212₁₆ Posts	prime pg(215) is congruent to the prime 21015781248582109976561479237247175760828678449588166559266766851 mod (2^214-1)

2018-12-17, 13:23	#69
enzocreti Mar 2018 2·5·53 Posts	51456 and 541456 are all coincidences? Last fiddled with by enzocreti on 2018-12-17 at 13:26

2018-12-17, 14:14	#70
enzocreti Mar 2018 1000010010₂ Posts	51456 and 541456 pg(51456) and pg(541456) are both primes. If I am right, both the probable primes are of the form 8400s+367.

2018-12-17, 14:52	#71
enzocreti Mar 2018 2·5·53 Posts	pg(51456) and pg(541456) the probable primes pg(51456) and pg(541456) end both with digits 55967! by the way 55967 is prime Last fiddled with by enzocreti on 2018-12-17 at 15:01

2018-12-17, 17:49	#72
enzocreti Mar 2018 2·5·53 Posts	51456 and 541456 as I said it is at least curious that pg(51456) and pg(541456) are both primes and 541456=700^2+51456 moreover 541456 and 51456 are both congruent to 111 mod 35

2018-12-17, 17:56	#73
enzocreti Mar 2018 2·5·53 Posts	...moreover... moreover (541456-13999)/7=75351 (51456-13999)/7=5351

2018-12-17, 18:31	#75
enzocreti Mar 2018 2×5×53 Posts	pg(51456) and pg(541456) mod(pg(51456),350000)=5967 mod(pg(541456),350000)=255967

2018-12-17, 19:33	#76
enzocreti Mar 2018 2·5·53 Posts	pg(215),pg(69660),pg(92020) and pg(541456) pg(215),pg(69660),pg(92020) and pg(541456) are the probable primes where k is a multiple of 43. Infact: pg(435) is prime pg(431620) is prime pg(432140) is prime pg(4312592) is prime now note that 5 (odd) is congruent to -8 mod 13 1620 (even) is congruent to 8 mod 13 2140 (even) is congruent to 8 mod 13 12592 (even) is congruent to 8 mod 13

2018-12-17, 20:04	#77
enzocreti Mar 2018 2·5·53 Posts	pg(67) and pg(51456) pg(67=671) and pg(51456=67768) are probable primes 1 is congruent to 1 mod 13 768 is congruent to 1 mod 13

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