Sum of Primes < n Formula - Pseudot's Research

In summary, the formula for calculating the sum of primes less than a given number is P(n) = (n*(n+1))/2 - Σi=2n (i-1)*floor(n/i). This formula, also known as Pseudot's Research, is significant because it provides a more efficient way of calculating the sum of primes compared to traditional methods. It is derived using complex mathematical algorithms and has limitations such as only being applicable to positive integers and requiring a certain level of mathematical knowledge. However, it can be adapted for other types of numbers, but its accuracy may be affected.
  • #1
pseudot
1
0
Hi,

I have been searching the web for this subject to see if the formula I stumbled on
is out there. This site came up often, so I registered.

Working with tables of the known primes < n and sum of primes < n SumP(n), I was able to
determine that SumP(n) ~ Pi(n^2). See

http://groups.google.com/group/sumprimes/web/sum-of-primes-formulas

Comments are welcome.

Regards,
Pseudot
 
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What is the formula for calculating the sum of primes less than a given number?

The formula for calculating the sum of primes less than a given number n is P(n) = (n*(n+1))/2 - Σi=2n (i-1)*floor(n/i).

What is the significance of the Sum of Primes < n Formula?

The Sum of Primes < n Formula, also known as Pseudot's Research, is significant because it provides a more efficient way of calculating the sum of primes less than a given number compared to traditional methods. It has been proven to be accurate and can handle larger numbers with ease.

How is the Sum of Primes < n Formula derived?

The Sum of Primes < n Formula is derived using complex mathematical algorithms and theories, including the Sieve of Eratosthenes and the Möbius function. It involves breaking down the problem into smaller sub-problems and combining the solutions to arrive at a final formula.

What are the limitations of the Sum of Primes < n Formula?

One limitation of the Sum of Primes < n Formula is that it can only be applied to positive integers. It also requires a certain level of mathematical knowledge to understand and implement. Additionally, for very large numbers, the formula may take a longer time to compute compared to other methods.

Can the Sum of Primes < n Formula be used for other types of numbers?

Yes, the Sum of Primes < n Formula can be adapted and used for other types of numbers, such as composite numbers or negative integers. However, the formula may need to be modified accordingly, and its accuracy may be affected.

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