Anyone have an easy way to learn the prime numbers from 1-100?

[united4ever]

My sons tutor tells us he needs to know these off by heart. He can work it out by doing a grid from 1 to 100 and eliminating the multiples of 2, then the multiples of 3 and so on but this is not really practical to do during the 11+ exam.

He can work it out for the first 5 or 10 numbers easily but when he gets up to the higher numbers it gets tricky and time consuming (again no good for an exam).

He could just learn the numbers but they are just quite a lot of numbers with no easy pattern so hard to remember.

Is there an easier way?

Well he knows these are not prime...
Even.
5 or 0.
You can add the numbers if they divide by 3... Not prime....
That doesn't leave many left..
Primes end in
Ends on 1,3 or 7....
He just has to have a quick think....

They end in 1, 3, 7 or 9 (apart from 1, 2, 3 & 5) so make a list of all of those from 1-99 and rule them out as you go. There aren't actually that many:

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.

One of the fascinating things about prime numbers is how they're distributed, so far we dont know exactly how. Which is why memorising them is seen as a good memory trick as there isnt a rule to follow

Just found a weird thing...
2,3,

1. Not 6.....7

11 not 12. 13 17 not 18.. 19 23, not 24 or 25 29 not 30 31 Not 35 or 36. 37 41 not 42. 43 47 not 48 or 49 53 not 54 or 55 59 not 60, 61 Not 65. Or 66, 67 71 not 72 73 Not 77, or 78, 79 83 not 84 or 85 91 not 92, 93 97 not 98 or 99...

Seems each side of 6 times table...

It's relatively easy to work out. Better to look at which aren't prime.

You know 1 isn't a prime number and 2 is the only even prime. Anything ending in 5 is divisible by 5 so (other than 5) any number ending in 5 isn't a prime.
So in each set of 10 you're left with only numbers ending in 1,3,7, or 9.

For seeing about factors you only need to look at the prime numbers (2, 3,7) as any number under 100 that isn't prime will have a factor that's under 10.
2 is obvious (evens)
Seeing if they're divisible by 3 is easy-add the digits together and if that is divisible by 3 then the first number is. (eg 93: 9 + 3 = 12 as 12 is divisible by 3, then 93 is)
7 he'll know the 7 x table up to 70. 77 is obvious, 84 and 98 are even, 91 is the only one he needs to remember.

So the only number he needs to remember is 91 (= 7 x 13)

So the only number he needs to remember is 91 (= 7 x 13)

This is why I wonder about the OP's tutor - presumably it's for answering questions of the type "which of these is prime?" and I can't imagine that takes so much longer than quickly testing the numbers when you know your times tables and witchend's tips - and that memorising takes away from time when you could be practicing that.

My sons tutor tells us he needs to know these off by heart

Why?

Honest just tell him 6 times table...use numbers each side of answer and just think if they work.

Honest just tell him 6 times table...use numbers each side of answer and just think if they work.

I think that's an approximation of witchends advice - and it looks like you need to add her rule 'So the only number he needs to remember is 91 (= 7 x 13)'

I honestly wouldn’t get him to spend hours and hours on this.

The NC expectation is to know them under 20, and be able to work 5em out to 100.

11+ is a bit different, I can imagine a VR question for example which might give the number sequence 2, 3, 5, 7...and they have to select what would be next (11). At most, this might cost him 1 mark. For the maths paper I’d say being able to work out quickly (using the tips above) would be fine.

I’d say there’s much more important things he could spend his time doing to prep for the 11+.

Another way of looking at this.
For numbers less than N, if they are not prime they will be divisible by a prime that is < Squareroot(N).

So under 100 any non-prime is divisible by 2, 3, 5, or 7
Divisiblity by 2, 3 or 5 is really easy to spot using rules, so the only prime he needs to check is 7. Presuming someone going for 11+ knows their times tables they know 7x7=49, and 7x11=77 so the only one they need is 7x13=91.

only read this next bit if you are at all interested

This gets more useful if wanting to check for primes a bit higher up, when it is also helpful to know the test for divisibility by 11, and also the fact that 1 less than a square number is never prime (eg if you know 18^2 = 324, you know 323=17x19.)

Surely 11+ questions should be geared towards whether the child can think not on rote learning something which is fairly useless.

It’s an odd suggestion from the tutor . Memorising lists like this might save you a few moments in maybe one question on a test even though to 100 is not that long. The complementary skill of knowing divisibility properties is handy and interesting though. Teentimes... suggestion makes a lot of sense as it reflects some real understanding.

It might have been a throwaway comment by the tutor about having to memorise them - I agree with lots of the methods above, instead work out which ones are not prime. If he knows the times tables well, he should find out the prime numbers fairly easily by elimination.

Many of the greatest unsolved mysteries in maths involve prime numbers. Goldbach's conjecture: "every even number greater than 2 is the sum of two primes"; and "what is the largest prime number"; I think both still unproven, unless somebody can put me right!

what is the largest prime number

There can't be a largest prime number:

• Take all the prime numbers you know and multiply them together.
• Then add 1.
• Either that number is prime, or you have missed a prime earlier.

@TeenTimesTwo Out of interest, did you read that one somewhere? You may be right, but that method's a new one on me!

I must have read it /learned it somewhere, possibly years ago, but it has to be right. (I had to do something about prime numbers for my degree in the computational maths module).

A number one more than all the primes you know about multiplied together can't be divisible by any of the primes, and therefore must be prime, or you have missed a prime out.
2x3=6, 6+1 =7
2x3x5=30, 30+1=31
2x3x5x7=210, 210+1=211

Professor Mathmo CD has a load of maths songs, including prime numbers www.amazon.co.uk/Professor-Mathmos-Fractions-Decimals-Essentials/dp/B00FA7VKZC?tag=mumsnetforu03-21

The pi one is a favourite of ours.