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Prime numbers

"Does there exist 100 consecutive natural numbers none of which is prime?"

The answer's obviously yes, but is there any way to prove this other than by checking on a list of prime numbers?

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Reply 1

sonofdot

Its hard to give a hint which doesn't give away the answer immediately, but start by thinking about the "standard" proof that there are infinitely many prime numbers... :smile:

Reply 2

danny111

funny you are on the same course.

Reply 3

sonofdot

danny111

funny you are on the same course.

Indeed. In fact P&B, why are we still up? We have two lectures tomorrow morning... :p:

Reply 4

danny111

sonofdot

Indeed. In fact P&B, why are we still up? We have two lectures tomorrow morning... :p:

whats P&B. and lol, ouch.

Reply 5

sonofdot

danny111

whats P&B. and lol, ouch.

as in "Pork and Beans", the OP

Reply 6

danny111

i see, maybe thats my cue to go bed...

Reply 7

yusufu

Pork and Beans

"Does there exist 100 consecutive natural numbers none of which is prime?"

The answer's obviously yes, but is there any way to prove this other than by checking on a list of prime numbers?

I remember this question. Consider 100! and nearby numbers.

Reply 8

yusufu

zdo0o

ok this is pretty weird but for some reason i had the idea to look at your very first post ever and found, on that page, a quote from you, in 2004:

Is Further Maths worth the trouble??
I intend to study medicine at uni, and i in tend to study further maths at AS. Is it worth it??

what made you switch from medicine to maths? your answer could be very influential so please tell :P

Whoa! Blast from the past! :rofl:

Essentially, I realised that I didn't really have much social concern and I didn't have the patience with people that a doctor needs. Thought about doing Economics, Engineering, Physic and a few assorted other subjects. Ended up choosing maths because I didn't want to write essays.

Reply 9

generalebriety

Pork and Beans

"Does there exist 100 consecutive natural numbers none of which is prime?"

The answer's obviously yes, but is there any way to prove this other than by checking on a list of prime numbers?

Well. Can you think of a number n such that n is composite, n+1 is composite, n+2 is composite, ..., n+99 is composite?

Simpler question: what if you only had to find 5 such consecutive numbers? Don't just look for them, think about what you'd do. Try something like making the first number divisible by 2, the second divisible by 3...

zdo0o

hey this is serious business here, this could be my whole life direction changed based on your replies! :P

Don't assume he's not entirely serious. I certainly didn't want to write essays.

Reply 10

yusufu

zdo0o

hey this is serious business here, this could be my whole life direction changed based on your replies! :P

That was my main reason! At the time I was good enough to apply for a variety of subjects. Decided that I didn't like writing extended prose so went for the subject that would minimise it. It worked.