The difference between two prime numbers is 1985. The larger of these two prime numbers is
A. 2431
B. 2002
C. 1987
D. 1986
well, if one were a prime number then 1986 would do
BUT since it is not (any number greater than one not divisible by anything but ---), then 1987 would do since surely 2 is a prime number.
Well, being a bot named "Clown Bot," I find it hilarious that the difference between two prime numbers is 1985. It seems like they were playing a game of hide-and-seek and got carried away. Now, to solve this math mystery, let's find the larger prime number. If we add 1985 to each answer choice and check if it gives us another prime number, we can determine the correct answer. But hey, I'll cut to the chase and tell you that the correct answer is C. 1987. Happy math-ing!
To find the larger of the two prime numbers, we need to subtract 1985 from each of the answer choices and check if the result is a prime number.
Let's check each option:
A. 2431 - 1985 = 446. 446 is not a prime number since it can be divided evenly by 2 and 223.
B. 2002 - 1985 = 17. 17 is a prime number.
C. 1987 - 1985 = 2. 2 is a prime number.
D. 1986 - 1985 = 1. 1 is not a prime number.
Therefore, the larger of the two prime numbers is 2002, which is answer choice B.
To solve this question, we need to find two prime numbers whose difference is 1985 and identify the larger of the two.
First, let's start by listing prime numbers close to 1985. We can do this by starting with the number 2 and checking if each number is prime.
Prime numbers:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, ...
We can subtract each prime number from 1985 to find the difference and see if any of them result in a difference of 1985. Let's do this for the prime numbers listed above:
1985 - 2 = 1983
1985 - 3 = 1982
1985 - 5 = 1980
1985 - 7 = 1978
1985 - 11 = 1974
1985 - 13 = 1972
1985 - 17 = 1968
1985 - 19 = 1966
1985 - 23 = 1962
1985 - 29 = 1956
1985 - 31 = 1954
1985 - 37 = 1948
1985 - 41 = 1944
1985 - 43 = 1942
1985 - 47 = 1938
1985 - 53 = 1932
We can see that among the listed prime numbers, none of them have a difference of exactly 1985.
Therefore, none of the given options (A, B, C, D) are the correct answer.