Prime

Number Theory Level 2

Two prime numbers sum to 86479. What is their positive difference?

The answer is 86475.

6 solutions

Nihar Mahajan
Oct 9, 2015

Since the sum of the $2$ prime numbers is odd that means one of them is even and the other one is odd. Thus one of the primes is $2$ . Therefore the other prime $=86479-2=86477$ . The difference between them $=86477-2=\boxed{86475}$

Very clear, concise explanation. I was going to write a very similar response, but why? Well done, sir!

Terry Warren - 4 years, 8 months ago

But can we call 2 even number. I'm confused, because though 2 is divisible by 2, but it also falls under divisible by itself and 1, being prime. Please correct my concept where I'm wrong.

Jyo Moy - 3 years, 3 months ago

Not sure if I understand what you're asking, but 2 is the only even prime because as you note, it fulfills the criteria for being even and the criteria for being prime, and any other number divisible by 2 would have to also be divisible by stuff other than two and one.

Psy Kosh - 3 years, 1 month ago

You are adding to the definition of prime by thinking that all primes are odd numbers. Being odd is not part of the definition of prime. All that is required for a number to be prime is that it is divisible by only 1 and itself. 2 fits that definition and thus is the only even prime number.

John T Reagan - 2 years, 11 months ago

Or ; if one has a list of primes then. start by subtracting the first prime on the list from the total, then the second, etc. If the difference is a prime you have solved the problem, if not try the next pime on the list. This solution works for ALL such problems, not just this one solution..

Richard Bauaman - 3 years, 2 months ago

My solution would reflect Nihar Mahajan’s elegant solution. No need to multiply words! James

James Malin - 3 years, 1 month ago

I love elegant answers! Well done!

John T Reagan - 2 years, 11 months ago

Allan Baguio
Nov 7, 2015

No even number greater than 2 is prime. And all prime numbers larger than 5 end in 1, 3, 7, or 9 since even numbers are multiples of 2 and numbers ending in 0 & 5 are multiples of 5. It is very clear that only number 2 subtracted from 86479 gives a prime number 86477 which ends in 7. So the positive difference would be 86477- 2 which is equals to 86475.

Ramiel To-ong
Oct 13, 2015

To make the sum an odd number, the number must be an odd and even, since only 2 is an even prime then we could get the correct ans. Parity of Integers

Yeah but he said its 4.That isnt even a prime number....

Rajko Spidkid Dragojević Dragojevic - 3 years, 12 months ago

Anu Sood
Dec 4, 2016

Sum of 2 even numbers is even, sum of 2 odd numbers is even. So one and only one of these numbers must be even. 2 is the only even prime number so the two numbers are 2 and 86477. Difference = 86477 - 2 = 86475 .

Ervyn Manuyag
Nov 8, 2018

2 is the only prime even number and 86479-2=86477 which is also prime so 86477-2=86475

Bhawana Paneru
Jul 7, 2017

It's very clear that in order to get 9 at the end while finding sum, a even no. must be at the end of one of the no. (since, odd + even = odd), & only even prime no. In the world happens to be 2. Hence, it is obvious that one no. is certainly 2. The other no. would be 86479 - 2 = 86477. Hence, difference = 86477 - 2 = 86475

Prime

The answer is 86475.

6 solutions

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