______ is the only prime number which can be expressed both as sum and difference
Answers
Answer: I think 5
Step-by-step explanation: There is only one prime number that can be written both as the sum of two primes and the difference of two primes. Find that number and prove that it is the only one. I've been thinking it could be 5? Since 2+3=5 and 7−2=5.
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Answer:
YES it would be 5. 5 can be expressed s a sum of two prime numbers [2+3] and also as a difference of two prime numbers [7-2]
Step-by-step explanation:
at first for the sum part we will have to consider that one number should be ven and another should be odd so that the sum would be odd beacuse if we take both odd prime numbers and add them then the sum will lead to an even number [sum of two odd numbers is even] and even number is divisible by two and hence it would not be a prime number
there fore we knew that we have to take such two numbers in which one is even and one is odd so that the resultant sum comes odd and we also have to add both prime numbers and an even prime number is 2
there fore we got one of the two number as 2 and the second number has many possibilities such as 3,5,11,17,... because 2 + [3,5,11,17,...] leads to a prime number but the prime number obtained from adding [5,11,17,..] with 2 leads to [ 5+2=7,11+2=13,17+2=19,..] but the problem is that the resultant sum obtained from adding 2 with [5,11,17,..] i.e [7,13,19,...] cannot be obtained as a difference of two prime numbers because they are all odd numbers and two obtain odd numbers from subtracting there should be one even and one odd number and here also the least even prime number is 2 so we got that in case of difference also 2 will be one of the numbers ad we know that in sum also 2 is one of the numbers and in difference also 2 is one of the numbers so we can conclude that the numbers when added to 2 will give x and similarly if a number subtracted by 2 will also give x so from this there i only one pair available [3,5,7] cause 3+2=5 and 7-2 is also 5 therfore we got the number 5 and it can be expressed as the sum of two prime numbers [2 and 3] and also as a difference of two prime numbers [7 and 2]
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