A is a prime number, and A 6, A 8, A 12, A 14 are all prime numbers, find all prime numbers A that m

Because 5+6=11

It's all prime numbers. Wish.

Here's what I think: one step at a time.

From a+6, a+8, a+12, a+14 are all prime numbers, you can know a lot of information: one is that a is an odd number, 2 is definitely not good, so these four numbers are all odd numbers;

The second is to subtract the smallest a+6 from the largest a+14, which is equal to 8, so we start from a+6 to a+14, a total of 9 numbers;

The third is that since it is a continuous 9 numbers, remove the even numbers, there can only be 5 odd numbers at most, and the end must be 1,3,5,7,9;

Fourth, a+6 must be greater than 8, so the odd number with 5 at the end must be a composite number, not a prime number, so only the number at the end of 1, 3, 7, and 9 is a prime number, which happens to be 4 numbers;

Fifth, except for the difference at the end, the previous items of these four numbers must be the same. If they are different, they do not meet the conditions given a+6, a+8, a+12, a+14 (they differ by 2, 4, 2), so we can write that these numbers must be b1, b3, b7, b9;

The sixth is to determine b, classified by multiples of 3, b = 3k + 1, 3k + 2, 3k + 3, obviously, from b7, b9, b can only be in the form of 3k + 1;

So a=b1-6=10(3k+1)+1-6=30k+5, because a is a prime number, k=0, so a=5

A cannot be divided by 5 to balance 1, because if a+14 is divisible by 5, it is not a prime number;

A cannot be divided by 5 to balance 2, because if a+8 is divisible by 5, it is not a prime number;

A cannot be divided by 5 and 3, because if a+12 is divisible by 5, it is not a prime number;

A cannot be divided by 5 and remainder by 4, because if a+6 is divisible by 5, it is not a prime number;

So a can only be a multiple of 5. Since a is a prime number, a can only be 5

is 5, if a divides by 5, 1 a+14 is divisible by 5.

If a divides by 5, 2 a+8 is divisible by 5.

If a divides by 5, 3 a+12 is divisible by 5.

If a divides by 5, 4 a+6 is divisible by 5.

So a should be a multiple of 5, and since a is a prime number, a must be 5

There is no formula for the prime number, and the source is balanced by the prime number, and the interval between the prime numbers is larger, so the method of bringing in one by one is chosen.

It was found that 7 is the smallest prime number that satisfies the question.

When a=7, hail is done, and the numbers in the question are 11, 13, 17, and 19

Because a+4, a+6, a+10, are all perturbed by the prime number of the finch.

Therefore, Xun A must not have a factor of 2, 3, and 5 multiples.

So the minimum number is 7

Knowing that the prime numbers a and a+ are both prime numbers, try to find the minimum prime number a that meets the requirements.

1.Let a=2 to verify whether 2+4+16+24+28 is prime; 2.If it is not satisfied, it means that the prime number with the smallest slippage may be greater than 2, then a+1, and then repeat the above steps; 3.

If the requirements are met, then a is the minimum prime number that meets the conditional call. a=5

a Calendar 4, a 8, a 10, a 14

The smallest is the Limb Destroyer Leakage Modification 3