A Prime Sum Of Primes

Number Theory Level 2

Find the smallest prime which is the sum of three distinct prime numbers.


The answer is 19.

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Sanyam Goel by sanyam goel , 26, India

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2 solutions

Achille 'Gilles'
Feb 11, 2016

First primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...

✘ 2 can’t fit the equation because odd + even + even = odd and beside 2, there is no odd prime.

✘ 3+5+7 = 15 Nope!

✔ 3+5+11 = 19 Eureka!

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Did you mean "beside 2, there are no EVEN primes"?

Hugo Eduardo Pérez Echeverría - 5 years, 4 months ago
Sanyam Goel
Feb 10, 2016

19 is the smallest prime which is the sum of three discrete primes (3 + 5 + 11).

1 Helpful 0 Interesting 0 Brilliant 0 Confused

It's good to note how you came to the conclusion that this is the smallest. For example, why couldn't 2 be used in this sum?

Eli Ross Staff - 5 years, 4 months ago

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It can't be used because then other 2 numbers will be odd so the sum will be even which won't be prime.

Kushagra Sahni - 5 years, 4 months ago

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what about 1+3+13? It sums up to 17 that is a prime number. Or you dont consider 1 as a prime?

Ivo Duarte - 5 years, 4 months ago

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@Ivo Duarte – Check out this wiki: is 1 prime?

Eli Ross Staff - 5 years, 4 months ago

@Ivo Duarte – 1 is neither a prime number nor composite. That's why 1 can't be used.

Aayush Gupta - 5 years, 4 months ago

why not (1+5+7) this is the smallest number!!!! because 1 is prime, 5 is prime and 7 also!!

Roger Djedje - 5 years, 4 months ago

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oooh sorry 1 is not prime....because a number is said to be prime when it is divisible by two distinct numbers 1 and itself... here the two numbers are not distinct , they are same (1 and 1) ...so 1 is note prime. thx Sanyam Goel for your lesson... i've considered this logic...

Roger Djedje - 5 years, 4 months ago

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Check out this wiki: is 1 prime?

Eli Ross Staff - 5 years, 4 months ago

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@Eli Ross – Before we start we should know what is a prime number... The say a prime number is a number only divisible by two distinct numbers (1 and the number itself)... Let assume 1 as a prime number then 1 is only divisible by 1 and 1 But 1 and 1 are not distinct mean they are same. So 1 is not prime... They are many rules about prime numbers but all converge to the sames results.

Roger Djedje - 5 years, 4 months ago

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