Largest Known Prime

1/25/2015

The largest known prime was discovered two years ago by Curtis Cooper.

It is a Mersenne Prime, 2^57,885,161 - 1.

When written in decimal form it is 17,425,170 digits long.

Of course it would be impossible to determine if a number that large is prime or not with out the use of a computer - well, in this case a bunch of computers.  When mathematicians are working on a project like this they are in competition with others for find another large prime to become the next "worlds largest known prime", but they are also competing in the world of computer science to test their algorithms for finding large prime numbers.

Because of this I have challenged myself to memorize this prime number in its binary form (because the computers that verified its "primeness" work in binary.

In binary it is 57,885,161 digits long.  And today I have finished memorizing all of them.  See below:










Wait for it!










Wait for it!










All 57,885,161 digits are "1".

Sometimes I even amaze myself.



David

Peggy Sue Does It Again

Tridecanacci Numbers: 

Gotta LOVE those Italian babes with mathematical skills.  Actually, this Italian babe immigrated from Italy when she was just 3 months old.  In fact she still speaks a little Italian - like "spaghetti", "pizza", "lasagna" and "raviolli" fluently.  She even know the Latin names of more body parts than I known the English names for.

Anyway she has developed a way of remembering the first 31 terms of the tridecanacci sequence, and she only has to remmber 1 number.  Then she takes its inverse, and converts it from a fraction to a decimal expansion.  The tridecanacci numbers are formed by a process similar to the Fibonacci numbers.  However it starts with 11 zeros, and 2 ones, after that each new term is the sum of the previous 13 terms.

1/999,998,999,998,999,998,999,998,999,998,999,998,999, 998,999,998,999,998,999,998,999,998,999,999 =

0.
000000  000000  000000  000000  000000  000000  000000  000000  000000  000000  000000  000001  000001  000002  000004  000008  000016  000032  000064  000128  000256  000512  001024  002048  004095  008189  016376  032748  065488  130960  261888…

The first 31 terms of the tridecanacci sequence (OEIS A168084).

She really loves the number 13.

David

Happy Birthday Peggy Sue

Happy Birthday

Happy New Year

Here is your first Interesting Number for 2015!!!

2015¹³⁷ = 

484,933,196,777,114,074,143,958,601,296,047,191,303,238,888,
328,493,788,893,417,124,636,461,282,535,535,197,030,813,992,
895,783,308,595,683,263,188,351,090,196,322,513,839,445,959,
271,157,649,518,041,540,183,146,596,171,102,022,830,089,650,
292,177,587,797,290,188,691,282,775,436,095,410,100,384,042,
181,289,460,837,638,885,592,477,530,746,168,643,702,581,379,
873,363,475,885,265,666,608,606,690,825,611,326,960,945,242,
512,576,880,699,871,340,946,150,843,683,152,340,103,534,181,
032,663,014,193,776,820,682,723,644,342,223,985,362,021,659,
566,308,072,475,404,600,254,478,282,295,167,446,136,474,609,
375

2015 = 4 + 8 + 4 + 9 + 3 + 3 + 1 + 9 + 6 + 7 + 7 + 7 + 1 + 1 +
4 + 0 + 7 + 4 + 1 + 4 + 3 + 9 + 5 + 8 + 6 + 0 + 1 + 2 + 9 + 6 +
0 + 4 + 7 + 1 + 9 + 1 + 3 + 0 + 3 + 2 + 3 + 8 + 8 + 8 + 8 + 3 +
2 + 8 + 4 + 9 + 3 + 7 + 8 + 8 + 8 + 9 + 3 + 4 + 1 + 7 + 1 + 2 +
4 + 6 + 3 + 6 + 4 + 6 + 1 + 2 + 8 + 2 + 5 + 3 + 5 + 5 + 3 + 5 +
1 + 9 + 7 + 0 + 3 + 0 + 8 + 1 + 3 + 9 + 9 + 2 + 8 + 9 + 5 + 7 +
8 + 3 + 3 + 0 + 8 + 5 + 9 + 5 + 6 + 8 + 3 + 2 + 6 + 3 + 1 + 8 +
8 + 3 + 5 + 1 + 0 + 9 + 0 + 1 + 9 + 6 + 3 + 2 + 2 + 5 + 1 + 3 +
8 + 3 + 9 + 4 + 4 + 5 + 9 + 5 + 9 + 2 + 7 + 1 + 1 + 5 + 7 + 6 +
4 + 9 + 5 + 1 + 8 + 0 + 4 + 1 + 5 + 4 + 0 + 1 + 8 + 3 + 1 + 4 +
6 + 5 + 9 + 6 + 1 + 7 + 1 + 1 + 0 + 2 + 0 + 2 + 2 + 8 + 3 + 0 +
0 + 8 + 9 + 6 + 5 + 0 + 2 + 9 + 2 + 1 + 7 + 7 + 5 + 8 + 7 + 7 +
9 + 7 + 2 + 9 + 0 + 1 + 8 + 8 + 6 + 9 + 1 + 2 + 8 + 2 + 7 + 7 +
5 + 4 + 3 + 6 + 0 + 9 + 5 + 4 + 1 + 0 + 1 + 0 + 0 + 3 + 8 + 4 +
0 + 4 + 2 + 1 + 8 + 1 + 2 + 8 + 9 + 4 + 6 + 0 + 8 + 3 + 7 + 6 +
3 + 8 + 8 + 8 + 5 + 5 + 9 + 2 + 4 + 7 + 7 + 5 + 3 + 0 + 7 + 4 +
6 + 1 + 6 + 8 + 6 + 4 + 3 + 7 + 0 + 2 + 5 + 8 + 1 + 3 + 7 + 9 +
8 + 7 + 3 + 3 + 6 + 3 + 4 + 7 + 5 + 8 + 8 + 5 + 2 + 6 + 5 + 6 +
6 + 6 + 6 + 0 + 8 + 6 + 0 + 6 + 6 + 9 + 0 + 8 + 2 + 5 + 6 + 1 +
1 + 3 + 2 + 6 + 9 + 6 + 0 + 9 + 4 + 5 + 2 + 4 + 2 + 5 + 1 + 2 +
5 + 7 + 6 + 8 + 8 + 0 + 6 + 9 + 9 + 8 + 7 + 1 + 3 + 4 + 0 + 9 +
4 + 6 + 1 + 5 + 0 + 8 + 4 + 3 + 6 + 8 + 3 + 1 + 5 + 2 + 3 + 4 +
0 + 1 + 0 + 3 + 5 + 3 + 4 + 1 + 8 + 1 + 0 + 3 + 2 + 6 + 6 + 3 +
0 + 1 + 4 + 1 + 9 + 3 + 7 + 7 + 6 + 8 + 2 + 0 + 6 + 8 + 2 + 7 +
2 + 3 + 6 + 4 + 4 + 3 + 4 + 2 + 2 + 2 + 3 + 9 + 8 + 5 + 3 + 6 +
2 + 0 + 2 + 1 + 6 + 5 + 9 + 5 + 6 + 6 + 3 + 0 + 8 + 0 + 7 + 2 +
4 + 7 + 5 + 4 + 0 + 4 + 6 + 0 + 0 + 2 + 5 + 4 + 4 + 7 + 8 + 2 +
8 + 2 + 2 + 9 + 5 + 1 + 6 + 7 + 4 + 4 + 6 + 1 + 3 + 6 + 4 + 7 +
4 + 6 + 0 + 9 + 3 + 7 + 5

2015 equals the sum of the digits of its 137^th power.

REFERENCES:

http://www.futilitycloset.com/2012/03/16/math-notes-101/

Happy New Year!!!

David