i think it's the only number where all the primes lower than it add up to it.
3+2 = 5.
take 7, all the primes lower than it are 2,3,5.
2+3+5 does not equal 7.
the number 4. all primes lower than it are 2 and 3.
2+3 does not equal 4.
does anyone know any other number that are like 5?
i don't think there is one. Am i right or wrong?
2007-04-09 07:30:20 · 2 answers · asked by mark_7908 1 in Science & Mathematics ➔ Mathematics
1 is not prime!
2007-04-09 07:37:10 · update #1
Yes, 5 is the only prime which equals the sum of primes less than itself.
To prove this is extremely difficult, but can be done. (Many theorems about primes are unanswered questions, however).
The proof involves looking at the 'density' of the primes and showing that there exists a particular 'abudance' of primes among the first 'N' numbers.
By that, we mean to show that for some k, there are more than k primes greater than N/k (where N is a selected prime >5). If we can show this is true then the sum of those primes > k(N/K) > N.
To get the proof filled in involves a lot of advaced number theory and calculus (primes are covered extensively in many graduate level number theroy texts if you are at that level).
Good luck and enjoy! Primes are fun to play and tinker with!
2007-04-09 07:57:40 · answer #1 · answered by chancebeaube 3 · 0⤊ 0⤋
1+2=3
2007-04-09 07:35:48 · answer #2 · answered by trojanknight_96 3 · 0⤊ 3⤋