How many zero divisors are there in \mathbb{Z}_{pq} and \mathbb{Z}_{p^2} when p and q are primes? How many integers from 1 to 19999 have exactly 15 divisors? How many positive divisors does 6! have? How many positive integers are le...
In how many ways can 50 be expressed as the sum of three different prime numbers? Prime Numbers: Prime numbers are one of the important concepts that is in mathematics. These numbers are basically not the factor by itself but are one of the factor of the composite numbe...
Additional differences include, but are not limited to "millia" vs. "milia". It is unfortunate that consistent spelling was not a hallmark of that era! When we codifying the rules for "The English name of a number", we were tempted to "improve" the system today. For example there are...
However, this performance is not good enough. There are 9592 primes below 1e5. And both codes check for all those primes. To enhance the performance we should first review sieving algorithms and reflect on the problem at hand: A number which is not prime is a composite number: It...
There are two sets of results. The first reports how many bytes per second can be processed for each algorithm, the second the times needed for sign/verify cycles. Here are the results on an 2.70GHz Intel Xeon E5. The 'numbers' are in 1000s of bytes per second processed.type 16 bytes...
Let’s say you write a program where you’re asked to check whether many numbers are prime; not just once. Even though our program above is highly optimized for that algorithm, there exists another way specifically suited for this situation: The Prime Sieve. ...
There are two sets of results. The first reports how many bytes per second can be processed for each algorithm, the second the times needed for sign/verify cycles. Here are the results on an 2.70GHz Intel Xeon E5. The'numbers'arein1000s of bytes per second processed. ...
They cover full frame, are super easy to adapt to many other mounts and never lose their value. You have a wide range of lenses to pick from and equally different price tags. You can either build a $1500 set or a $10000 set and you’ll always impress with the results. They’re ...