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

I probably should shore up the approah starting at 53, there now being quite adigression, but 61 is the 18th prime and the inversion of 19, and I have 18 prime curios accepted and 1 pending (if I don't count the one they still list as pending under 0 that was replaced by the recently accepted one under 5).

Sorry about the missing 'c' and missing space.

Anyway, I can continue with 67--using the same digressive path I've used since 43--by noting that the one curio I have pending involves Mersenne primes and the first of the curios for 67 is that Mersenne incorrectly stated that 2^67-1 is prime.

Continuing more ordinarily, 71 is in sequence in 177719, 73 is the large prime factor of the 365 whose notice started it all, and 79 is also in 177719. I could add that 71% of the Earth's surface is ocean, one of the curios, and then give a list of the curios that are suggestive to me and why from 79, but it's a little superfluous right now so I won't. If I don't find a better way to get 97 in than as the reverse of 79 when I get to it, I'll count that, but now the main tasks are to get 83 and 89 into the mix first.

As you may recall, starting with 29 I moved to some external research. Though the thing on 17771 being the 30th number that makes a palindromic prime when sandwiched between 10 and 01 is nice, and the fact that I was just finding my curio on 5 at the same time kind of allowed me to add on 29 and 31, it is a little bit of a glide from really intrinsic facts. Well, I've come up with another way to get 23 and 29 that connect the two nicely. The numbers of different numbers that are a substring of 37765 and 177719, respectively, are 23 and 29. Now, I was pretty satisfied up through 47 as it was, and really I'm not at all unhappy about how I've gotten all that I have--all primes less than 100 except for 83 and 89--but this little added gravy is nice.

I was just thinking that I had goofed in the last post, but those 23 and 29 are correct. I just got a really nice way to get 83, and another example of how it appears I might be mediating these results in general. I was going through PrimeHunter's (Jens Kruse Andersen's) prime curios. The one with most intrinsically coincidental-looking digits begins 300000. It also ends 1777931, which is really just a couple of minor tweeks off from being 177719 (and it also happens to be prime). In the middle of these two strings of digits is 22410. What did I first ask myself about the whole long number? What its largest prime factor is, hoping that it was 83. It is.

That is, I asked that not about the whole long number but about the middle 22410. The long number is prime.

You will make it.

Hi, PAL. How is everything?

Mmm ok I suppose, given my internet connection isn't working most of the time.

How are you? ok I hope, still pushing back the boundaries of primes I see.

Really, I'm not all that well. Aside from my own lack of dosh being a major major problem, arguing with people over at rationalskepticism.org about my coincidences is causing me headaches right now. People just say they believe they're true without demonstrating the slightest hint of comprehension and insist that I'm arguing unsoundly using their own specious and totally disconnected rhetoric.

I think you need the then you can see everything all at the same time.

Neat as the way that I got 83 is, I realized a short time ago a very mundane way to get it that's quite intrinsic. It's the largest prime factor of 37765.

Just a little report on additions to Prime Curios. Only one of my recent submissions has (very recently) been accepted so far, with the other still waiting in the queue. The one accepted is for 53: 'This number is an emirp in 11 straight bases, from base 30 through base 40. Is any other number an emirp in as long a chain of bases?' The ones in queue are one that was added to the one already accepted for 4, dealing with the primes generated in taking the 4th prime that generates a prime twice in going from both bases 2 and 3 to base 10 when translation is effected in going from bases 5 through 25 to base 10; one on 109 being an emirp first in base 13 (all smaller primes other than 2 and 3, which aren't emirps in any base, being emirps in some base smaller than 6); one on 769 being the first prime that isn't an emirp until base 10; and the one dealing with Mersenne primes that have a prime number of digits in base 7 that I indicated I will spell out here in the event it's rejected. Nothing new here on the base-10 coincidence front, by the way.

Submitted another nice result: '110111: The first composite in repeated base-4-to-base-10 interbase translation beginning with 5 is the 5th term, this near repunit which reads in binary as 5 times the first term.'

Submitted another one: '701: The first prime that translates from bases 2, 3, 4, 5, and 6 to base 7 as primes....' I just listed the 5 translations and said I'd leave the matter of how nice the collection is to the reader to figure out. It's pretty nice.

Correction: Make an exception of 2 and it's right.

I just thought of this because the ID# for the one I just submitted--on 31193--was 10739. That curio is about translation from base 4 to base 10. It's the 4th prime to do it 4 times prime, and with 5, 29, and 73 as the first 3, I noted the ratio (5*29*73)/31193=0.3393390. As gravy, the 5th iterate upon 31193 has smallest prime factor 2393 and the 5th term after 31193 is 43093.

That is to say, the 5th term, 1st after.

My most recent 3 curio submissions only have one that's particularly coincidental. The first are just the largish numbers that translate 4 and 5 times as primes from bases 2 and 3, respectively. Today's was that 2351 is the first prime for which 3 distinct primes less than it can be found such that as many as 17 of the 24 concatenations of all 4 are prime, noting that 2357 is the next prime and that the previous one, 2347, is the last of only 12 that achieve the high water mark of 16. I mentioned what the 3 primes going with 2351 were--2179, 83, and 17--but I didn't bother explicitly pointing out the way 17 is highlighted. I'll either submit a 6-fold base-4-to-base-10 translation tomorrow, if the computer finds one by then, or I'll submit another coincidence I found. That's that if you take the list of all the primes that translate from base 5 to base 6 and then also base 4 to base 6 and then also base 3 to base 6, as represented in base 10, through the first to also translate again from base 2, then when you throw out all the 1s in the final digits (They have to be for a simple reason) you're still left with a full 19 out of 57 digits being 1 for no real theoretical reason. As for the one I might still submit in its place, when I do submit that one I can connect it with the next one I submit. There are a huge number of 5-fold translations preceding the first 6-fold one. By contrast, the from-base-5 result I have is that the first prime that translates 8 times manages to also do so a 9th. These aren't the sort of coincidences I've been on about, but they make a nice contrast.

Ah, spoke (wrote, typed) too soon. I got the 6-fold base-4 result, and the huge number is 211. I need to do a little theoretical thinking here. This actually does smack of being a bit of a coincidence. It's like picking 100 people at random and having them all have different birthdays or something. I mean, consider that the very first prime that's eligible for consideration, 5, not only translates once but four times, and contrast that and that it's followed up with 29 and 73 with this.