social pharmacy d-pharm 1st year by Pragati K. Mahajan
Prime numbers
1. PRIME NUMBERS
N O. 1 T O P I C T O B E S T U D I E D
T H O U G H 1 I T S E L F I S N O T A P R I M E
2. WAY S TO FIND NUMBE R OF PRIME
NUMBE RS
The notion of how many prime numbers come before a particular number
‘n’ which is raised to consecutive powers ‘y’, starting from 1, is given by the
two variables x1 and x2.
Where x1 and x2 determine the range of the required prime numbers
before n^y.
The results tend to the numbers which we would get on counting.
However, after a certain numbers, this method of counting becomes
impossible to use, indicating the indispensability of the aforementioned
variables.
3. X1 = n / ln(n)y
X2 = n / ln(n)y - 1
where n = the given number
y = the power to which n is raised
ln = Natural Logarithm
5. W A Y T O F I N D N U M B E R O F P R I M E N U M B E R S
T H E TA B L E
Number
(n)
Power to
which 2 is
raised(y)
Number of
prime numbers
(p) Less than the
given numbers
X1=
n
───
0.6931y
X2=
n
───
0.6931y-1
2 1 0 1.44 (-)
4 2 2 2.88 5.17
8 3 4 3.84 7.41
16 4 6 5.77 9.02
32 5 11 9.23 12.97
64 6 18 15.38 20.26
128 7 30 26.38 33.23
256 8 46.16 56.32
512 9 82.07 97.74
1024 10 147.74 172.65