Every student, who has learned programming, must have written a program to determine whether a given positive integer is a prime number. Basically in order to determine whether a positive integer n is prime, we search for any number in the range [2, n − 1] which can divide n. Some of you would have designed a slighly better implementation where you search √ for any divisor of n from the range [2, n ]. Does either of these two implementations correspond to an eﬃcient algorithm ? Ponder over this question deeply. Let us try to design an eﬃcient algorithm for a problem which looks as simple and innocent as the problem discussed above. First, we give a deﬁnition. Deﬁnition 1. A positive integer is said to be bit-sum prime if the sum of the bits in its binary representation is a prime number. For example 6(110), 14(1110) are bit-sum prime numbers, whereas 29(11101) is not a bit-sum prime number. Design and implement an algorithm which receives a 64-bit integer n and outputs the count of all the bit-sum prime numbers less than n. Test it for a really large number, for example, execute your algorithm for 123456789123456789. Hint: Your algorithm/program is NOT supposed to enumerate all the bit-sum prime numbers. Instead, it has to just report the count of all the bit-sum prime number. Hence the output will be just a single number. Notice that you will have to use clever programming skills also in this problem.

every art is beautiful and so is the art of algorithm design ...

...Partial Sums of the Riemann Zeta Function
Carlos Villeda December 4th, 2010
Chapter 1 Introduction
1.1 Riemann Zeta Function
In 1859, Bernard Riemann published his paper “On The Number of Primes Less Than a Given Magnitude”, in which he deﬁned a complex variable function which is now called the Riemann Zeta Function(RZF). The function is deﬁned as: ζ(s) = Σ 1 ns (1.1)
Where n ranges over the positive integers from 1 to inﬁnity and where s is a complex...

...my family (guys) try and tell me to do something they say things like “no guy is gonna want a girl who can’t cook or want a girl who bites her nails or want a girl with such an attitude” as if my only purpose for living was to please some guy
I also need feminism because when my little cries, gets upset, or happy or expresses any emotion he’s told by family members (also guys) to stop acting like a girl. As if being a means keeping things bottled up and being tough all the time or that...

...my seat
belt, ignited the car and we set off to Dhaka University area, one of
the areas with widest lanes. Since it was early morning, the roads
were free of congestion and I drove very comfortably and
confidently. Simultaneously, I was also a bit nervous.
I drove around many wide and almost empty lanes of Dhaka University for half an
hour and then through Nilkhet we started heading towards Dhanmondi. Reaching
Dhanmondi, we found an empty ground many beginners go for...

...Many people have eaten dim sum without actually knowing what it is. For one thing I know is that I never knew what it was when I was younger. I just thought it was just Chinese food, never thinking that it had a background of its own. Who knew it would have such an interesting background, or meaning? Dim sum is more than just Chinese food; it has its own story and customs.
Before I started researching dim sum I already knew a few things about it. I...

...
FP061 – BUSINESS INFORMATION TECHNOLOGY 061
STUDENT ID : 700013988
NAME : SHEREEN ALEXANDER
GROUP : 1C3
ESSAY TOPIC : DEPENDENCY OF HUMAN ON COMPUTERS
TABLE OF CONTENT
#1. Introduction………………………………………………………………………………….…………..3
#2. What are computers?.................................................................................................................3
#3. The evolution of...

...What is the closed-form expression for the below sum of Geometric
Progression (GP) sequence, S n ?
S n a aR aR 2 ... aR n
(1)
where R is called the common ratio (between consecutive terms) of the GP
sequence.
The reason why we want to derive a closed-form expression for S n is for the sake
of calculating the summation, or otherwise we need to add all terms one-by-one
together, which does not make a sense if the number of terms is huge, say a
million terms!...

...Dennis Thrane
NT 1210
Unit 4 Lab
10/12/2014
Exercise 4.1.1 Why are standards so important for NICs, connectors, and media? Use your textbook and Internet research to justify your answer.
The physical level determines how the 0 and 1 bits are identified. So both ends need to know the voltage range for a 1 and for a 0. If they used different values then the data would be lost, or the voltage at the destination may be so high that the current delivered to the destination could...

...DIVISIBILITY RULES
Rule #1: divisibility by 2
A number is divisible by 2 if it's last digit is 0,2,4,6,or 8.
For instance, 8596742 is divisible by 2 because the las t digit is 2.
Rule # 2: divisibility by 3:
A number is divisible by 3 if the sum of its digits is divisible by 3
For instance, 3141 is divisible by 3 because 3+1+4+1 = 9 and 9 is divisible by 3.
Rule # 3: divisibility by 4
A number is divisible by 4 if the number represented by its last two digits is...