h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

I just got another pretty nice base-10 coincidence. The first primorial--product of all primes up to a certain point--that has a string of 10 or more digits all the same is the product of the first 2^13 primes.

ABRACADABRA results in two emirps! 1218131412181, 1812141318121, 1182141311821 and 1281131412811 are all prime.

Oh, a big one I recently found that I thought had already been posted here: For k=2 through at least 12, the only concatenations of the first k primes that are also products of k distinct primes are ten for k=10. I don't have the list with me at the moment. I'll post again once the result for k=13 is done.

Hi Julzes!

I thought you might be one of the few people to appreciate the coincidence:

The number of this Edited Entry on Prime Numbers A26107751 just happens to be the product of two prime numbers!

Well that is not what I would call easy reading; I even had to remind myself of what a complex power is.

Euler did a lot of stuff, and I thought Gauss was 21 in 1801, but I don't know.



My brain don't work anymore; how do you find the zero's of a zeta function.

Hardly a coincidence for a relatively small number to be a semiprime, Rudest Elf. I will have to look at it later. I'm losing lots of weight walking from one public computer to another and eating next to nothing. It's cool to lose weight and see that the problem I had with a long walk several years ago was precisely caused by my weight being too high; however, it's not so good to be flooded with email concerning very real possible solutions to my personal problems--including this limited access--and not have the internet service to sort them.

So, Julzes, how many semiprimes are there between 10,000,000 and 99,999,999?

Cor

I have just discovered that it doesn't pay to doubt Julzes.

The number of semiprimes between 10,000,000 and 99,999,999 according to my calculations (well, not exactly all mine) is approximately 15.5 million, or 17.25%!!

So, not such a coincidence, after all.

Nope, definitely doesn't pay to doubt Julzes.

That's 69 quarters of a percent, Rudest (and G.H.Hardy's cab number in the famous anecdote about his visits with Srinivasa Ramanujan is 4 more than 1725 as well) .

*hospital visit

I think I have a new sequence of some fascination (damn sure, actually): Powers of the arithmetic-geometric mean of 2 and 3 (and the default precision of PARI/GP was/is informative too).

*new to me, at least. Seems a likely thing to have been looked at by someone else before me, but I don't know.

In the last week I have had a large number of submissions accepted at the Prime Curios! website, most having significant coincidences attached to them. They may be viewed at http://primes.utm.edu/curios/ByOne.php?submitter=Merickel by clicking on the ones marked 'updated'.

Congratulations

I'm studying number this year with the Open University. I don't think I'll ever get as deeply into it as you have, but I now understand a bit about multiplicative functions, quadratic reciprocity and the like

"number theory" that should read.

I think Julzes is on a mission. You know I was a bit amazed to find that the best in mathematics did the same as Julzes does.

You are welcome to make your mind up if it is useful to your aims, follow Julzes because somehow knowing a big number is comfortable.

I used to wonder why people go to such trouble to find those enormous Mersenne primes. I guess it's because they don't yet have a big enough sample to sift through, to try to spot patterns in them.

I think the reason as regards Mersenne primes is that you can make history with little effort (or knowledge these days) and there is a lot of unused computational capacity that may as well be doing something.