Today's Favorite Mega Number

[kruoli]

Originally Posted by MattcAnderson

Check out this mega prime 1,753,961.

As you found out by yourself, 1,753,961 is not a prime. You only slightly missed a "mega prime" (1,753,963)!

[Dr Sardonicus]

Originally Posted by MattcAnderson

<snip>Check out this mega prime 1,753,961.
<snip>

Not only is the number (as previously pointed out) not prime, but "mega prime" is all too easily confounded with the term "megaprime," which denotes a prime with at least a million decimal digits.

[Dr Sardonicus]

Originally Posted by MattcAnderson

Hi again all,

My new favorite seven digit number is 9,999,999.
<snip>
9,999,999 = 3*3*239*4649.
<snip>

This brought to mind the following example illustrating the properties of the blocks of digits in the repeating decimals for k/p, k = 1 to p, p prime. Here, p = 239, a factor of 9999999. Since 239 divides 9999999, the repeating decimal for k/239, k = 1 to 238, has period 7. The blocks of digits may be further classified by the following 34 numbers:

[1004184, 2887029, 2050209, 1464435, 1046025, 1757322, 1255230, 1087866, 1506276, 3054393, 1380753, 1966527, 3765690, 2635983, 1882845, 1631799, 1422594, 1589958, 1129707, 4979079, 3556485, 3974895, 2426778, 4476987, 1213389, 2384937, 4560669, 1924686, 2803347, 2343096, 1673640, 1171548, 2008368, 4058577]

Each of these 34 numbers is the 7-digit block for the repeating decimal for a fraction k/239, for some k between 1 and 238. In each case, the value of k is obtained by dividing the 7-digit number by 41841. For example, dividing 1004184 by 41841 gives 24, and 24/239 = .10041841004184...

By cyclically permuting the digits in each block, the seven-digit blocks of the repeating decimals for the remaining fractions k/239, k = 1 to 238, are obtained.

For example, cyclically permuting the digits of the first block gives 0041841, and .00418410041841... = 1/239; permuting again, 10/239 = .04184100418410..., 100/239 = .41841004184100..., 44/239 = .18410041841004... and so on.

Each of the numbers is the smallest cyclic permutation of the block of digits whose leading digit is non-zero (i.e, a number between 1000000 and 9999999).

[MattcAnderson]

Hi all,

Today's mega number is 3,152,781

And due to a modern computer tool we can see that this number can be written as 3*3*137*2557.

Matt

[Uncwilly]

There is no need for a modern computer to factor that number.

[Dr Sardonicus]

Originally Posted by Uncwilly

There is no need for a modern computer to factor that number.

Especialy in light of (my emphasis)

Originally Posted by MattcAnderson

<snip>
Today's favorite Mega number is 7,122,222.

And by inspection, we can see that the prime factorization is 2*3*3*3*131893.
<snip>

If you can do that "by inspection" (and determining 131893 is prime by TF requires dividing 131893 by all primes up to about 360), I'd say 3152781 could also be done "by inspection."

[MattcAnderson]

Hi all,

Today's favorite mega number is 3,157,793.

My computer tool, Maple, tells us that this number has a full prime factorization of 53*59581.

Regards,
Matt

[MattcAnderson]

Hi again all,

Today's favorite mega number is 2,456,921.

My computer has Maple software, so, with the ifactor() command, I can see this number has full prime factorization of 53*151*307.

Regards,
Matt

[MattcAnderson]

Hi all,

Today's favorite Mega number is 4,692,781.

It's full prime factorization is 2677*1753.

Regards,
Matt

[MattcAnderson]

Hi again all,

Today's favorite mega number is 9,876,567.

The prime factorization of this number is 3*103*31,963.

Have a nice day.

Matt

[MattcAnderson]

Hi all,

This mega number is 2,345,676.

Due to Maple, we see that this number can be written as 2*2*3*47*4159.

Enjoy

Matt