215 and 541456

[enzocreti]

215 is congruent to 1/125 mod (9/10^3)


541456 is congruent to 1/125 mod(10^3/9)

[enzocreti]

(541456-2^4)/2^8=2115

2115-215=19×10^2

2115 and 215 are congruent to 6 mod 19

and (215-6)/19=11
(2115-6)/19=111

so rearranging
(111*19+6)*2^8+2^4=541456

11*19+6=215

[LaurV]

Wow, that is quite interesting, if you add all the ascii codes in "enzocreti" you get 'e'+'n'+'z'+'o'+'c'+'r'+'e'+'t'+'i' = 101+110+122+111+99+114+101+116+105=979.

Now you add 1, and divide by 2, so (979+1)/2=490.

490=76+97+117+114+86.

Coincidence? Or are you my lost twin brother?

(and DON'T EDIT MY POST! - use reply/quote if feel like you want to reply!)

[retina]

Originally Posted by LaurV

Wow, that is quite interesting, if you add all the ascii codes in "enzocreti" you get 'e'+'n'+'z'+'o'+'c'+'r'+'e'+'t'+'i' = 101+110+122+111+99+114+101+116+105=979.

Now you add 1, and divide by 2, so (979+1)/2=490.

490=76+97+117+114+86.

Coincidence? Or are you my lost twin brother?

Hehe. Numerology at its finest.

Originally Posted by LaurV

(and DON'T EDIT MY POST! - use reply/quote if feel like you want to reply!)

Okay, I promise to follow your edict.

[LaurV]

Originally Posted by retina

Okay, I promise to follow your edict.

Well, to be fair, it was not him who edited my posts, but it was storfly, my memory plays silly jokes on me. Here only the first sentence after the quote is mine (and I was talking about him ), the rest he added. Which is kind of rude to edit people's posts to change their meanings. But that is my punishment I deserve for replying to these kind of blogs and talking to bots, hehe, and in my mind is a complete amalgam of all these people/bots talking nonsense on the forum, so I think I am forgivable for the confusion I did...

Anyhow, prevention is the mother of wisdom. Nastratin Hogea used to beat the child before sending him to fetch water, so he be careful and avoid breaking the pitcher, and when asked why, he replied "after he breaks the pitcher, no point to beat him anymore, that won't fix the pitcher"...

[enzocreti]

(541456-(307*8-1000))/2^4/5^4=54


(51456-(307*8-1000))/2^4/5^4=5


pg(51456) and pg(541456) are probable primes


1456=307*2^3-10^3


541456-215=307*1772-1763-1000

[enzocreti]

pg(215) and pg(541456) are prp


307*2^4-(41*43+10^3)=215*10-1


so 2150=307*2^4-1763-10^3+1


5414560=307*2^4-1763-10^3+1+10*1763*307

541456-215=307*1772-1763-1000

[enzocreti]

pg(215) and pg(541456) are probable primes with 215 and 541456 =0 mod 43


the maximum power of 2^k for which pg(541456)-pg(215) is divisible is k=65


65 is also the number of digits of 2^214-1


curio


(pg(541456)-pg(215))/3/2^65/23=1234...
a number that starts with 1234...


N=((2^541456-1)*10^162995+2^541455-(2^215-1)*10^65-2^214)/2^65/69=1234...


N is congruent to 216=6^3 mod 307


541456=50*215*41+307*8*41+10




541456=11520*47+16
69660=1786*39+6
92020=3539*26+6


47,39 and 26 are the solutions x to the systems



1763x+215 is congruent to 0 mod 86, 1763x+215 is congruent to 6 mod 13
1763x+344 is congruent to 0 mod 86, 1763x+344 is congruent to 6 mod 13
1763x+903 is congruent to 0 mod 86, 1763x+903 is congruent to 6 mod 13


the residue ends always with digit 6 (infact 6 and 16)


541456=11520*47+16
69660=38*47*39+6
92020=3539*26+6


where 3539 is a prime of the form 1763k+13...note that 3539 is the smallest prime of the form 1763k+13


215, 69660, 92020, 541456 are of the form 1763s+r
and they are congruent to 227 (or 228 in the case of 215 odd) mod 13


it is surprising that one solution to the system

1763x+387 is congruent to 0 mod 86
1763x+387 is congruent to 6 mod 227 is x=307

the numbers 1763s+387 are congruent to 10^m mod 41 like 215, 69660, 92020 and 541456

1763=227+3*2^9