CONJECTURE (PROBABLY FALSE) THAT CANNOT BE DISPROVEN UNTIL QUANTUM SUPREMACY COWS WILL COME HOME
 

pg(k) is the number (2^k-1)*10^d+2^(k-1)-1 where d is the number of decimal digits of 2^(k-1)-1
pg(215) and pg(541456) are probable primes.


215 and 541456 are multiples of 43 and 10 mod 41.


541456 is 215 mod 307.


I conjecture that when k is multiple of 43 and pg(k) is prime and pg(k) is 10 mod 41, then k is 215 mod 307.


for k of the form 1763s+215 and pg(k) prime, k is 215 mod 307

[QUOTE=enzocreti;522698]
I conjecture that when k is multiple of 43 and pg(k) is prime and pg(k) is 10 mod 41, [/QUOTE]

I thank you want to say:
I conjecture that when k is multiple of 43 and pg(k) is prime and k is 10 mod 41

ok
 

yes...my english is awful...

Let \(C_0 = 2\), \(C_i = 2^{C_{i-1}}-1\).
So:
C1 = M2 = 2[SUP]2[/SUP]-1 = 3, [B]prime[/B]
C2 = MM2 = M3 = 2[SUP]M2[/SUP]-1 = 2[SUP]3[/SUP]-1 = 7, [B]prime[/B]
C3 = MMM2 = MM3 = M7 = (some nerdy formulas in a row) = 127, [B]prime[/B]
C4 = MMMM2 = MMM3 = MM7 = M127=(more nerdy formulas) = 170141183460469231731687303715884105727, [B]prime[/B]
C5 = MMMMM2 = MMMM3 = MMM7 = MM127 = crazzy large number with trillions of trillions of digits (do you think I counted them? :loco:)

[B]Catalan conjecture[/B] (we don't know the answer, but most people believe it is false):[B] C5 is prime.[/B]

Let: C6 = MMMMMM2 = MMMMM3 = MMMM7 = MMM127 = MMcrazzylargenumberwithtrillionsoftrillionsofdigits

[B]LaurV's QUANTUM conjecture[/B] (most probably false, but I will post it anyhow, to show to all the guys here how clever I am, and better add something about quantum age because every mention to quantum stuff attract people like every mention to shit attracts flies, and if possible, write it with UPPERCASE to show everybody I don't give a prime about their feelings): [B]C6 is prime. [/B]

See you disprove this, quantum or not...

Conjecture
 

if pg(k) is prime and k is of the form 1763s+215, then k is 215 mod 307...or I don't know if this is equivalent


when pg(k) is prime and k is of the form 1763s+215, then 10k is congruent to 1 (mod 307)