Researches Involving Researcher Numbers

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This Entry details many strange results obtained by manipulating several researcher numbers beginning with my own. The basis for doing this research was to explore the possibility that we are here following a plan, and that our researcher numbers would be an avenue to display this fact. After getting here to h2g2 and struggling for a while to get a couple of Entries through Peer Review (A54649146 and A54782832), I settled down to try some other things. The first main thing was exploring the nature of my researcher number, U14075709. I began this with the hootoo tradition of getting 42 from my number. The way I found first--and I haven't really tried the traditional way--employs base 13 in the spirit of Douglas Adams's joke on this base. Simply adding the digits of my number gives 33, and reading this as a base-13 number gives 42 in base ten.

The thing I did next yielded something rather surprising. I considered U14075709 as now a base 42 number with the 'U' counting as the digit for 30. What I found was that the resulting number back in base ten is the product of the square of 69 times a large prime that ends 693. Considering the Family and Brainstorming Unit of The Miracle Scheme in my personal introduction in the light of a certain sexual position that couples not wanting children or to have to use birth control, I found this rather interesting, especially given that I already had a small relationship between the digits 6 and 9 in the form of the equation (365+1/4)^2=3^7*61+9/16. My Entry A55164279 details what my next step was--taking the polynomial that my researcher number (with the 'U' as 30) generates consideration of for looking at the number in any base, and plugging in all the numbers I could and factoring. This seems like overkill now, but one really interesting thing came of that.

To me, it has been quite clear that I have been mediating or channeling something, and my discovery of what happens with my researcher number as a base-39 number is an instance of this. The result of the prime factorization there is the base-ten evaluation 160711600297491=3^2*17856844477499. For some reason, I converted the large prime back into base 39, and I really only did this in this one case. The result reads U14075709=9*3D4UDUZHE. The large prime, then, actually reads phonetically as something of an English sentence (or question): 3-D for you does he. The first thing I thought about this was concerning what we know of the likelihood that there are 11 dimensions to our physical reality only three of which (not including time) do we perceive (This comes from what is called Superstring Theory or M-Theory). If we assume the traditional God of the whole Universe--my thinking went--then our three spatial dimensions could be God's design for us. I reject this--and God as a 'he'--in favor of this being just a question that needs to be resolved and also perhaps a kind of order to me (the factor 9 if I understand my place in religious history correctly) to stick with h2g2 until I can contribute things with three-dimensional graphics. Since I spent a little time as a senior in high school studying holography (or pretending to--I was really there to be near a certain female) at the Franklin Institute, this latter seems appropriate.

There really doesn't seem to be anything else in my own researcher number, though this was quite a lot. It didn't stop with my own, though. Post 176 of the Peer Review thread for A54782832 yielded a subject that ultimately, I believe, is (so far) the most important of my purely mathematical results in the construction of Entry A55643259 out of the A-number of another Entry. The author of that Entry, I found, is a prime in base 42 (his researcher number with 'U' as 30, that is). He himself took his researcher number, converted it from base 10 into base 13, and found that there is a forum under the title 'Deleted' with that number. As his last act was to withdraw from the thread we were relating to each other in (on account of my position that there is no God of the whole Universe), I will leave these facts as easily doable research rather than being specific in naming him and the thread in which our discussion took place here. An open question for me is whether the polynomial deriving from his number is sort of unique in that it is prime for 0, 1, 2 and 3, and then not again until 26 and then 42.

The fellow just discussed and I were in a thread together along with the host of the particular journal while all of these discoveries were being made. You can find the discussion we had if you know that his number is 22 times a prime in base 42 and that the polynomial associated with the prime factor (in base 42) is next a prime when 69 is plugged in. That prime in base ten: 626923369697323. I have taken this as another little sign relating the digits '6' and '9'. The polynomial involved is prime at -41 and 42, but not in between, and this is certainly a rarish thing, as inquiries at wikipedia's mathematics help desk have established. The next negative value at which it is a prime, -63, isn't very interesting.

I have only looked at a few more people's researcher numbers in any detail at all, and not that much, but what I got was interesting. One value was just good for a little joke on a person having 666 in her U-number, and that's all it amounted to. Another user was 11*101*39839 after reading his as base 13, and there was some other stuff I didn't bother to write down that looked like more evidence relating the digits '6' and '9'. The last story hardly involves the researcher number itself at all, but it has been a significant jumping-off point to demonstrating mediation on my part (with a little interesting mathematics thrown in).

Clive the Flying Ostrich is one of my sceptics. At one point I jokingly threatened to look into his researcher number like I had done with myself and in a friendly way with the fellows who ended up being prime and 22 times a prime. He told me I could feel free to 'abuse' his researcher number, so I did. I just did the very simplest thing and factored the number in base ten. This gave the prime 18913, and from that point I was basically done with his researcher number. What I saw in this that interested me was 1981. A problem that I worked out in high school and repeated a couple of times rather recently was to get as many numbers as possible up to 100 out of the digits of 1981 using the four basic functions, exponentiation, the root symbol, an overbar for repeated decimals, and an exclamation mark for factorial (You can get everything except 94 this way, if you're up for a challenge; and proof that you can't get 94 is something that would be really challenging).

1981 was a pretty big year (good and bad, for me and the world), and something about the numbers 11981, 21981, 31981, etc., stimulated me to look at the factorizations of these numbers up well past a prefix of 100. The only thing that I will relate is what happens right as we get to 100. The numbers 931981, 941981, 961981, 971981, 991981 and 1001981 are prime, and it is a simple matter to show that the most you can get out of eight consecutive prefixes is six primes (every third number must have 3 as a factor). Well, it turns out--and this was a pain to demonstrate the way I did it--that if you take the prefixes in order from 100 down to 93, then 1981 is the first number that brings you all the way down to 94 in the question of whether the numbers are all prime, and it is the only four digit number that is also prime down to 93. Only one five-digit number and four six-digit numbers, as a matter of fact, can be prefixed with 93, 94, 96, 97, 99 and 100 to generate all primes. Only one of these numbers can be used to generate also a prime with 91 prefixed, and this number is 132667.

What I did next is the most astonishing thing of all. Taking all five of the aforementioned five- and six-digit numbers, I checked Entries, Fora and Users here to see if there was anything with those numbers. It turns out that there was nothing except for the special case of 132667. There are two users who have apparently done nothing with their personal spaces that 132667 pointed to: U13266777 and U13266793. The polynomial 30x^8+x^7+3x^6+2x^5+6x^4+6x^3+7x^2+7x+7 yields a number ending in 777 only for numbers congruent to ten and forty-two modulo one thousand. My immediate check of the first U-number as a base-42 number revealed another number ending the same way. Just as an indication of how unusual this is, the same thing can only be said about the other U-number only when the base is ten added to a multiple of one thousand.

Well, that's about it. I will relate the basically unrelated remarkable results found at wikipedia's math help desk by PrimeHunter that when 9955031915073901 has 78, 79, 82, 84, 85, 87, 90, 91, 93, 94, 96, 97, 99 or 100 prefixed to it the number is prime; and that when 1989530586646177 is prefixed with 0 (no prefix), 1, 3, 4, 6, 7, 9, 10, 13, 15, 16, 18, 21 and 22, each of the resulting numbers is prime. I was absolutely astonished with both of these amazing results, but, like PrimeHunter said, there is a reason behind his name.

I have one final note to add, as it turns out. After completing this, one particularly irritating-to-everyone researcher led me to look into her U-number. Nothing much came from the usual factorings, but I noticed when in the process of converting to base 13 that the last shown digits (by the calculator I happen to be using) of the natural logarithm of her number are 7774777. This ties in nicely with what I discovered in the paragraph before last.

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