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Greatest prime number that can be represented as both the sum of 2 prime numbers as well as difference of 2 prime numbers?
We will use the fact that if p prime, a divides p, then a = p or a = 1.
Then if p + q = r, for primes p, q, r, then one of p,q,r is even, or all three are (consider mod 2). p = q = r = 2 clearly doesn't work, and p + q = 2 doesn't work for primes p,q >= 3. So without loss of generality p = 2, then r = q+2. r is also the difference of two primes, r = s - t. Again considering mod 2, knowing that r is odd, one of s or t is even (and so equal to 2). If s = 2 then r is negative, so t = 2, and we have q + 2 = r = t - 2, so t = q + 4.
So we have q, r = q + 2 and t = q + 4 all prime. By considering q mod 3, one of them has a factor 3. If a prime has a factor 3, it is equal to 3. So q = 3, as q + 2 = 3 or q + 4 = 3 mean q is not prime. So, r = q + 2 = 5. Therefore, 5 is the only prime that can be represented as both the sum of two primes and the difference of two primes: 5 = 2 + 3 = 7 - 2. Since it is the only one, it is the greatest.
What else can I help you with?
What is a range?
the difference between the greatest and the least number in a set of numbers
What is range in numbers?
it is the greatest number in a set minus the least number in the same set. the difference is the range.
What is the difference between the greatest and the least 2-digit prime numbers?
Greatest 2 digit prime number is 97. Lease 2 digit prime number is 11.
What is a real number represented by?
The set of real numbers is represented by a fancy script "R". However, real numbers are just represented by a number (be it integer, rational, irrational, or otherwise). The key here is that it is not a complex number (number containing the imaginary number "i").
What is the difference between greatest 7 digit number and the greatest 8 digit number?
The difference is 90000000
What is a range?
the difference between the greatest and the least number in a set of numbers
What is the difference between the greater number and the least number?
In a set of numbers, the difference between the greatest and the least is called the range.
What is the greatest prime number that is the sum of 2 prime numbers and is the difference of 2 prime numbers?
5
What is range in numbers?
it is the greatest number in a set minus the least number in the same set. the difference is the range.
What is the greatest prime number that can be representedas both the sum of two prime numbers and as the difference of two prime numbers?
5
What is the difference between the greatest and smallest 2-digit prime numbers?
11 is the smallest 2-digit prime number and 97 is the greatest 2 digit prime number, so their difference is 86
What number is the greatest common factors of a number under 50?
If we are trying to find the two numbers less than 50 with the greatest common factor, we need to pick two numbers with a larger difference between them, since the greatest common factor between two numbers cannot be greatest than the difference between the two numbers. To create a large difference, we will want one number to be close in value to 50. And, for the greatest common factor, we want the other number itself to be the greatest common factor. The greatest common factor that the larger number can have (since it is larger and thus cannot be the greatest common factor itself) is the number which is half its value. So, if we choose the even number closest in value to 50, we get 48. Then, if we take half of it, we get 24. The greatest common factor of 24 and 48 is 24. This is the largest possible greatest common factor of a pair of numbers less than 50.
How do you teach the difference between negative numbers?
Put all the numbers - zero, positive, negative - on a number line. Positive numbers to the left, negative numbers to the right. The difference between any two numbers is represented by the distance between them. Thus putting numbers on a number line is a great visualization tool.
How do you calculate the range between two numbers?
The range of two numbers, or a set of numbers (more than two numbers) is the difference between the greatest number and the smallest number (numerically). Hope this helps!
What is the greatest prime number that can be represented as both the sum of 2 prime numbers and as the difference of 2 prime numbers?
5. this is 2+3 and 7-2. this is the highest one i could think of. after this it becomes impossible, because you have to use two or you are adding 2 odd numbers. which makes an even, which cannot be prime.
What is the difference between the greatest number and the least number?
The difference between the greatest and least number is the range.
What is the difference between the greatest and the 2 digit least prime numbers?
Greatest 2 digit Prime number is 97. Lease 2 digit prime number is 11.
