The 15th Conjecture

Author : Spanu Dumitru Viorel Address: Street Marcu Mihaela Ruxandra no. 5 , Bucharest , Romania Phones : +40214131107 +40723880545 Emails : [email protected] [email protected] [email protected]

The 15th Conjecture There are infinitely many prime numbers amongst the natural numbers of the form : pn

+

(ln pn ) 2

or

pn

+

(ln pn ) 2

.

where ln is the

pn

is the nth prime number ;

logarithm in base (ln pn ) 2

e .

is the floor function

and

(ln pn ) 2

is the ceiling function .

David Hilbert in 1912

I want to quote the genius David Hilbert : Wir müssen wissen, wir wissen We must know , we shall know Nós devemos saber, nós saberemos Nous devons savoir, nous saurons Debemos saber, nosotros sabremos Dobbiamo sapere, noi sapremo Πρέπει να ξέρουμε, ξέρουμε Wij moeten het weten, zullen wij het weten