Prime numbers

A Thinking Task

I think of a prime number, and add it to the next larger prime number.

I continue with this twice more. I have now worked out the sum of four consecutive primes. This total comes to 202.

What was the prime number I first thought about?

Solving this will involve some trial and error or guesswork. There could be less hard work if you think about it first of all.

It should take a lot less than five minutes to find the answer ~ you will know yourself whether it is right or wrong.

If some of the words are new or strange ~ here is some help ~

Prime Numbers ~ are numbers which do not appear as answers in your multiplication tables ~ the times tables. You have to do a fair bit of trial and error to work out prime numbers. Is 17 a prime number? Try 2x8=16, 2x9=18...it is not divisible by 2. Next try ~ 3x5=15 ~ 3x6=18 ~ nor 3. Next try 5x3=15 ~ 5x4=20. ~ Next try 7x2=14 ~ 7x3=21. Next is 11...and that does not work either.So 17 is a prime number. All this is much easier if you know your times-tables well

Sum ~ This word is often used when talking about questions ~ problems ~ tasks ~ as in 'I am doing some sums'. Mathematicians use the word to mean specifically to mean adding-up tasks. The sum of the digits two, three, four is 2+3+4 and the sum ~ summation ~ is nine.

Consecutive means 'following on in sequence'. You might ask 'What sequence?' Well~ that has to be made clear at the same time as using the word consecutive. 13~17~19care consecutive prime numbers ~ starting with thirteen. 12~14~16~18 are consecutive even numbers, starting a 12.

Solve ~ means 'find the solution' to the task ~ puzzle ~ question ~ problem

Trial and error ~ guesswork. One way to tackle this problem would be to think of any prime ~ say 13 ~ then move on to 17 ~ add them up ~ and so on. That would be your first guess or try or trial. It will ~ sadly ~ be in error for the question as set. Some people are able to work out the smaller prime numbers very quickly ~ they have maybe even learnt them. Larger primes take more thought ~ or trials and successes perhaps!

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