Challenge

[flouran]

Originally Posted by Mini-Geek

Yeah, the crackpot index doesn't exactly tailor to this sort of crank.

Yep, that's exactly why I was unsure at first as to whether or not science_man_88 was a crank.

[retina]

Maybe science_man_88 is just posting in the wrong thread?

http://mersenneforum.org/showthread.php?t=7450

[akruppa]

science_man_88,

I told you not to post in threads outside of this one. Do it again and you'll be banned for a week.

Alex

[science_man_88]

Who asked why they all end in 7 or 1 ? if I'm right it's because 2^odd will always end in 2 or 8 and hence -1 will give 7 or 1 . in base 2 the same ending happens every 4 exponents 2^1=2 2^(1+4)=32 etc. if it has to be a prime I believe in 2^p, p must be modulo 10 to a prime( or at very least an odd).

[R.D. Silverman]

Originally Posted by science_man_88

Who asked why they all end in 7 or 1 ? if I'm right it's because 2^odd will always end in 2 or 8 and hence -1 will give 7 or 1 . in base 2 the same ending happens every 4 exponents 2^1=2 2^(1+4)=32 etc. if it has to be a prime I believe in 2^p, p must be modulo 10 to a prime( or at very least an odd).

It is time that someone applied my crank index:

(1) 10 points for trying to discuss any subject for which
you have not taken a course, or read at least one book.

(2) 15 points for not using standard mathematical terminology.

(3) 15 points for failing to define your variables and their
domain.

(4) 20 points for trying to generate a discussion instead of
asking a question when it is clear that you do not understand
what you are trying to discuss.

(5) 25 points for failing to do a web or literature search
before posing an idea or question.

(6) 35 points for elementary mistakes in high school level
mathematics.

(7) 50 points for trying to invent new mathematical
terminology.

(8) 50 points for trying to "reinvent the wheel". An extra
10 points for reinventing a "square wheel" (e.g. a 'new'
algorithm that performs more poorly than existing ones)

(9) 50 points for posing poorly defined problems, or
for posing problems which show a lack of BASIC understanding
of elementary aspects of the subject you are trying to
discuss.

(10) 100 points for both trying to invent new terminology
and failing at the same time to rigorously define what
that terminology really means.

(11a) 100 points for posting a 'conjecture' in which it is clear that you have
not bothered to test it yourself via numerical example. Especially if trivial
counter-examples are available.

(11) 200 points for even trying to pose a solution to a
well-studied problem in which you are not an expert.

(12) 500 points for trying to claim that knowledge of the
state-of-the-art "gets in the way" of creativity.

(13) 1000 points for any comparison of yourself to any
well known mathematician, or for trying to point out that
some prior mathematican worked in some area in which he/she
was not trained as if this were an excuse for your doing the
same.

[science_man_88]

1) So math isn't a course ?
2)only things I haven't really heard before are "hence" and "to a"
7) once again only things I haven't really heard before are "hence" and "to a"
10) this is stupid that's the third part in which you make points from terminology.
11) I've done the math to show that all odd exponents will produce a 1 or 7 ending( just never showed it).
13) never once have I compared myself with anyone famous.

[retina]

Originally Posted by science_man_88

...
13) never once have I compared myself with anyone famous.

science_man_88, that was just the index, R.D. Silverman was asking for someone to apply it. Perhaps you would like to make a score for yourself?

[science_man_88]

no thanks has anyone tried this before?:

#7 ends in 9
#21 ends in 9
#35 ends in 9
#49 ends in 9 ?

also

#7 starts in 1
#21 starts in 9
#35 starts in 1
# 49 starts in 9 ?

also

if you look at the number of digits of the exponents

2,3,7, first sequence of difference is 1,4 the next one seems to be either 7 or 9 if this pattern holds true ? if the 9 part is true then the next is 9 so 9+7 or 16 digit primes starting and ending in 9 ( how many ?) oh and did I have to mention it's likely over 43 million ? so 16 digits is 90 quadrillion so somewhere around 90 quadrillion and 9

[CRGreathouse]

Originally Posted by xilman

An excellent reason for writing prime-finding programs is to educate oneself. It was a component in my education on several occasions. I was about 12 years old the first time I implemented such a program, based on the SoE, and it was executed entirely on paper. I still have the notebook which contains the output.

I remember my first such program, around the same age (11). It was written in QBasic and found all primes up to x in time O(x^2 log^2 x) with a high big-O constant. How is it possible to run that slowly? Hint:

IF INT(N/K) = N/K THEN D = D + 1

By 12 I learned that you only needed to test up to the square root, bringing the exponent down to 1.5, and I had figured out several clever (to me) optimizations. I understood but never implemented the Sieve (exponent 1) until much later; I wasn't too good with arrays.

Years later, I read Bernstein's paper giving a sublinear algorithm. My mind was entirely blown.

[flouran]

Originally Posted by CRGreathouse

Years later, I read Bernstein's paper giving a sublinear algorithm. My mind was entirely blown.

Sieve of Atkin, eh?

I remember when I was amazed around the age of 12 when I had plotted theoretical super strings using Euler's Beta function (it was Susskind who first realized that particles could be "stringy" and some Italian physicist who years before had noticed that the Beta Function seemed to describe the strong nuclear force pretty well. My memory is a little clouded here though since I haven't read up on string theory since I was 12).

[CRGreathouse]

Originally Posted by science_man_88

I've done the math to show that all odd exponents will produce a 1 or 7 ending( just never showed it).

Good, your conclusion is correct. Let's see the proof (it's not too hard and you said you did it already). And while you're at it, what about

• the approximate number of 16-digit numbers starting and ending in 9 (how many middle digits?)
• the approximate number of 16-digit primes starting and ending in 9 (use the prime number theorem and the fact that all such numbers are odd)
• the approximate time needed to test a 16-digit prime exponent starting with 9 using, say, a single core of a Core II; see http://mersenne.org/report_benchmarks/ (look at an exponent at size S, 2S, and 4S and guess a rough rule)
• the approximate time needed to test all 16-digit prime exponents starting and ending in 9 to see if they're Mersenne exponents (using, say, a billion quad-core Core IIs)

These should be within your ability, if you work on them in sequence.

Originally Posted by science_man_88

2,3,7, first sequence of difference is 1,4 the next one seems to be either 7 or 9 if this pattern holds true ? if the 9 part is true then the next is 9 so 9+7 or 16 digit primes starting and ending in 9 ( how many ?) oh and did I have to mention it's likely over 43 million ? so 16 digits is 90 quadrillion so somewhere around 90 quadrillion and 9