Belphegor's Prime

computation
you only need to check like, 10^15 numbers max

>>8310723
surely there's an easier, quicker way

>>8310726
there isn't

>>8310726
Find one and get a Fields Medal for free!
Or you can tell me the way and i pay you 5€.

>>8310726
youre not even an undergrad are you?

I know how to do it in constant time, but I'm holding the answer from the world for cryptography and humanity's sake

>>8310689
There's a 1/2 chance of it being prime (it's either a prime or not)

>>8310797
>implying

>>8310689
Multiply it out.
Write a program to calculate primes.

>>8310689
Wolfram says it is prime.
There are several database that contains prime numbers up to much larger numbers that this one.

>>8310767
2 is not a factor
3 possibly
5 is not a factor
7 possibly
There must be a way to determine
possible (and not-possible) factors
which would reduce the search time.

>>8313489
3 is not a factor, idiot.

>>8313489
easy to show 3 is not a factor

>>8310803
>1/2 chance
>not knowing 50% probability
gtfo fgt pls

>>8313506
>>8313519
[claimed]

>>8310689

The below is simply an elaboration on the first post, which as per usual is the best post.

The number, which I shall refer to as [math] B [/math] is, in relative terms (which are the pertinent ones for the present consideration), slightly larger than [math] 10^{30} [/math] . Thus, it stands to reason that its square root is something slightly larger than [math] 10^{15} [/math] , since of course [math] \bigg( 10^{15} \bigg)^{2} = 10^{15} 10^{15} = 10^{15 + 15} = 10^30 [/math] .

An algorithm for verifying that [math] B [/math] is in fact prime (or otherwise composite) goes exactly like this. Notice that I do not claim that it is an efficient algorithm, only that it is an algorithm that works:

1) compute the square root of [math] B [/math], up to some convenient, non-zero decimal place. This is a straightforward exercise that can be done by hand, by a human, in a few minutes. Take the ceiling of this number, so that what you have in the end is one more than the integer part of the true square root of [math] B [/math]. Call this latter number [math] c [/math] . You will find that in relative terms, [math] c [/math] is a bit larger than [math] 10^{15} [/math] , as has been discussed.

2) [math] c [/math] has been chosen according to the above procedure, so that we know how to count every natural number up to and including [math] c [/math] . That is, we know how to check every natural number up through the square root of [math] B [/math] , plus one, which latter is no problem (in relative terms). Thus, we have definitely established a range 1-c of natural numbers covering everything up through [math] B [/math] 's square root, plus one. The primes in this range are all that we need to check against [math] B [/math] , for if we suppose for discussion that [math] B [/math] is composite, then it must have a prime divisor less than its square root. If we should find that such is not the case, then we are forced to conclude that B is prime. Thus...

[cont.]

3) Compute a list of every prime number from 1 up through c, inclusive. Store this list. The prime number theorem can be used to estimate the quantity of prime numbers that one should expect in this list at about 2.8953 x 10^13 - it suffices to produce this estimate to apply the PMT to 10^15.

4) Divide [math] B [/math] by every prime number in the above list (or some equivalent arithmetic check). If a non-zero integer part should result in the quotient in every case (or equivalently by way of suggestion, if in every case a given p should be multiplied by an appropriate m, and then later an appropriate m+1, and both products should fall on either side of [math] B [/math] , neither product being equal to [math] B [/math] itself), then the algorithm must conclude per the above that [math] B [/math] is prime.

5) Be sure to ask a computer or supercomputer to do all of the above, since life is too short.

6) Offer suggestions for improvement on the above. Consider starting here: https://en.wikipedia.org/wiki/Primality_test Notice that at a skim, the later language seems to suggest only probabilities in many cases, that is, quickly finding candidates or similar, and not doing the above presumably necessary bruteforcing, which perhaps ultimately becomes necessary in certain cases. In particular, the Lucas test looks at a glance as though it may be applicable in this case, to get around the above tedium.

Or better yet! We are told by all of wikipedia, wolframalpha (simply ask WA to factor() the number) and Dr. Clifford Pickover, who named the prime, that it /is/ in fact prime. I would imagine that WA has simply stored this isolated fact as a cute meme-fact of which it is aware, without bothering about direct computation once it knows what number it has got in front of it. Review of Pickover's page about the number and the below link puts us onto Harvey Dubner and finally /an article/, which should directly answer the OP's question.

[cont.]

>>8314408
you only need the floor of the sqrt you faggot

Since all of these reputable sources are agreed, and are quite insistent that [math] B [/math] is in fact a prime, this implies one of two things:

Someone got computer time to do the above bruteforcing, or some other tedium along the above lines, or

There is a nicer, pure mathematical technique for establishing as a piece of knowledge, that [math] B [/math] is in fact prime.

The relevant blurb is right there on Pickover's page:

http://sprott.physics.wisc.edu/pickover/pc/1000000000000066600000000000001.html

"The Prime of Belphegor can be written concisely using the notation 1 0(13) 666 0(13) 1, where the number in parentheses denotes the number of consecutive zeros. Harvey Dubner determined that the first 7 numbers of this type have subscripts 0, 13, 42, 506, 608, 2472, and 2623 [see J. Rec. Math, 26(4)]. When will humanity discover the next in this series? " (That is, that these numbers /are prime/, apparently - anon.)

And despite its meme-listicle appearance, the below page seems to give similar actulaly helpful context on how the number was established to be prime:

http://www.atlasobscura.com/articles/how-a-mathematician-turned-an-obscure-number-into-a-scary-story

The point is that there is a small sequence of numbers of the above-indicated form which are presumably established to be prime via mathematics, presumably without any of the above bruteforcing. The point being that OP has actually been onto something this whole time and (if the article pans out, I haven't checked it yet) that the people going (hurr computation) may yet be proven as charades, in which case I would have to retract my fpbp comment. But I haven't checked yet.

The below page gives the article name, haven't seen a link yet. trying to zero in on same.

http://charlesashbacherreviews.blogspot.com/2016/07/contents-of-volume-26-journal-of.html

>>8314434

True and yet, at the same time, somehow, trivial. I did declare right at the start that what I wrote was an effective procedure, not that it is efficient. :^)

Anyway I'm off to work now (couldn't dredge up the article itself in a few minutes) but now we know exactly where to look:

Journal of Recreational Mathematics, Volume 26, Number 4:

“Palindromic Primes with a Palindromic Prime Number of Digits,” by Harvey Dubner

(and what appears to be a Pickover article immediately following, perhaps stopping just short of a collaboration on-paper):

“Some Observations on Reversed Numbers and Palindromes,” by Clifford A. Pickover

I welcome the thread to look into the above, whether by visiting an RL college library or if you can get it online somehow. cursory googling did not turn up the article itself, especially the first one by dubner.

Dubner (nice name for all this) also has a few other related articles on the above link, one of which is in this same journal issue. work now.

>>8313737
retard, all numbers that are divisible by 3 have a digit sum that's divisible by 3. This number's digit sum is 20, which isn't divisible by 3.

>>8314509

"Are you SURE about that?", said John Cena.

Consider the number six as written in binary. It is expressed as 110.

Now, consider the sum of these digits, whether expressed in binary, or in decimal. Recall that "summing the digits" simply entails uncoupling each numeral from its contextual place in the orignial string, no matter the base that you happen to be working in, considering each as a separate number, and them summing those numbers so expressed. Thus in both cases of both bases, the sum of the digits is the quantity two, which number has for its expression 10 in the binary system, and of course 2 in the decimal system.

But this latter expression, whatever its base, is of course immaterial; the point is that the number six, which is divisible by three, does not have the property that the sum of its digits is a multiple of three.

You're about to whine that it should be obvious that you were referring to base ten, and probably it is, but the point is that you are missing an important, non-trivial declaration about which base you are working in, and in which number base the statement is true.

>>8316014
Okay favelaboi

>>8316109

I notice your lack of a rebuttal, where one is required and warranted in this case.

File: 1470517841611.jpg (42KB, 400x400px) Image search: [Google]

42KB, 400x400px

>>8316014

>>8313737
666 is divisible by 3, so 666*10^14 is congruent to 0 mod 3. 1 is congruent to 1 mod 3. 10^30 = (3*3+1)^30, which, if you binomially expand this, creates 31 terms, 30 of which have a factor of 3, so those 30 are congruent to 0 mod 3, and 1^30 = 1, which is congruent to 1 mod 3. 0+1+0+1=2 mod 3. The number is congruent to 2 mod 3, so it is not a multiple of 3.

>>8310689
1 + 1 + 6*3 + 1 = 21
Therefore, the number is divisible by 3.

>>8316248

look again numbnuts.

>>8316014
The question is posed in base 10, it would be extraordinary to arbitrarily change the base.

>>8316248
you fucking primitive sponge

>>8316425
>>8316807
Without any evidence to the contrary, I assumed the × operator referred to addition. You guys will understand when you get to college.

>>8317706
>I'm retarded but I'll claim college people mix up symbols
fuck off. you know exactly what x means

>>8317706

I have a four year math degree and such a notation never showed up during my formal education. So nope, you don't get to wriggle out of having been dumb. And no, the quality of my education has not been wanting, so don't bother about that route

Not even in polish notation does such nonsense crop up; there, the everyday arithmetic operational symbols continue to be used in their same contexts (the ones that you, all of us know perfectly well despite your cute defense to the contrary), albeit in different locations with respect to the operands.

The other contexts of multiplication usually devolve to elementary number multiplication at some point. What is essential in the dot product for instance is multiplying each term, then summing, likewise taking the products of matrices. There is not a commonly-used sense of the diagonal cross-symbol in intermediate mathematics that exclusively entails addition, to the exclusion of multiplication (or, repeated addition). And for you to pull out a goofy meme-one still puts the lie to what you're trying to do, exactly because its rarity relative to the other contexts simply proves the unreasonableness of your having assumed that context before the others. But you didn't actually do that because you simply flubbed a 1 and you know it.

>>8317765
>I have a four year math degree
wow, good for you! :)

>>8317807

Ikr? :3

>>8317825
youre a qt c:

>>8317765
>I have a four year math degree

lol

>>8317706
I hope your genetics get permanently destroyed by some enormous trauma because holy shit your stupidity can't be allowed to pass down.

>>8318160
A pretty typical reaction to abstract mathematics. Don't worry, you'll learn all about things like operators and derivatives when you're a little older.

>>8318324

I'm not that guy and we are all agreed that your troll continues to suck. But not hard enough that we aren't biting.

You have solved a heroin trip with my works in HEX. You have made rays all over, proving a line exemption in math as we feel.

>>8310689
>all that stupid superfluous math
>not just typing 1.000000000000066600000000000001 x 10^30
why do you hate scientific notation, anon?

>>8318570

Scientific notation has the double disadvantage of being ugly and looking inexact, as if it is a physical approximation of some kind. You could have literally written the actual number itself using a strict subset of the keystrokes that you expended in this post.