Did you know : PRAMIYA* NUMBER

Did you know : PRAMIYA* NUMBER

o  If (P-1) ! + 1 mod P^2 =0   , where P is a prime, then P is a PRAMIYA* NUMBER , PRAMIYA NUMBERS are 5 & 13

Now check ExteMia**

o  In the prime factorization of (P-1)! +1 we will get prime with single power except P=5 or 13 (where P = Prime) 22! + 1 = 23*Q*R*... 

USES :  

o  Total number of factors N! + 1 is in the form of  , except 4!+1 & 12!+1

o  Total number of factors of P! + P are divisible by 3 but not by 9 (due to  in prime factorization), where P is prime except PRAMIYA NUMBER (5 & 13) which is divisible by 4 due to P^3 in prime factorization)

*PRIME + AMIYA **Extension by Amiya

Did you ever notice this

Did you ever notice this:-

Step 1: Take any number N , whose sum of digits

Step 2: Multiply N by 11 and say resultant as M , N*11 = M

Step 3: Reverse the digits of M and say it P

Step 4: Divide P by 11 and say it Q , P/11 = Q

Step 5 : Check N & Q , Q is reverse of N  

E.G.

Step 1: N= 12113

Step 2: 12113*11 = 133243 = M

Step 3: 342331 = P

Step 4: 342331 / 11 = 31121= Q

Step 5 : Check N & Q , Q is reverse of N