Register to reply

Sum of Squares, Distinct Primes

by abiyo
Tags: distinct, primes, squares
Share this thread:
abiyo
#1
Nov12-10, 01:44 AM
P: 43
Hi All,

So I was just wondering if there is a formula for the number of ways a number can be written
as a sum of squares?(Without including negatives, zero or repeats). For example 5=2^2+1^2. (There is only one way for 5).

Second question along this line is: In how many ways can a number be written as a sum of primes(i.e a sum of two primes, three primes ).

Third Question: 10=2+3+5 Thus 10 can be written as a sum of maximum three prime numbers; no more. Is there such an upper bound for other numbers? I was doing this for
small numbers but would be interesting to see if there is some sort of pattern or theory

Thanks a lot
Abiyo
Phys.Org News Partner Science news on Phys.org
Scientists discover RNA modifications in some unexpected places
Scientists discover tropical tree microbiome in Panama
'Squid skin' metamaterials project yields vivid color display
CRGreathouse
#2
Nov12-10, 02:16 PM
Sci Advisor
HW Helper
P: 3,682
Quote Quote by abiyo View Post
So I was just wondering if there is a formula for the number of ways a number can be written
as a sum of squares?(Without including negatives, zero or repeats). For example 5=2^2+1^2. (There is only one way for 5).
This is complicated, see
http://mathworld.wolfram.com/SumofSquaresFunction.html

Quote Quote by abiyo View Post
Second question along this line is: In how many ways can a number be written as a sum of primes(i.e a sum of two primes, three primes ).
About exp(2 Pi sqrt(n/log n) / sqrt(3)). I don't imagine there is a nice closed-form formula.
http://oeis.org/A000607

Quote Quote by abiyo View Post
Third Question: 10=2+3+5 Thus 10 can be written as a sum of maximum three prime numbers; no more. Is there such an upper bound for other numbers? I was doing this for
small numbers but would be interesting to see if there is some sort of pattern or theory
Can you be more specific? This is ambiguous.
abiyo
#3
Nov12-10, 02:34 PM
P: 43
Thanks CRGreatHouse. Sorry the last question is worded badly. What I wanted to ask is

Pick an integer n. We want to find partition of n into its prime parts. For example
10=7+3
10=2+3+5

There are two partitions of 10 into primes. The first one involves two primes, the second
involves three primes. The claim then is that 3 is the maximum partition of 10 into primes.
3 is the longest partition.

Now let me choose some arbitrary integer(large n). I might have x number of partitions of
n into prime parts. I want to determine the longest partition. (how many prime numbers
are involved at maximum).

Is there a formula or a theoretical treatment?

Thanks a lot once again
(My English is terrible. sorry if this is confusing again)


Register to reply

Related Discussions
Pythagorean Primes and Gaussian Primes, divisibility question Linear & Abstract Algebra 3
Sum of distinct primes Linear & Abstract Algebra 5
Factors of product of n distinct primes Linear & Abstract Algebra 7
Distinct primes Calculus & Beyond Homework 1
Numerical Methods - Linear Least Squares, Non-Linear Least Squares, Optimization Math Learning Materials 0