Answer to Google Billboard

e = 2.7182818284 5904523536 0287471352
        6624977572 4709369995 9574966967
        6277240766 3035354759 4571382178
        5251664274 2746639193 2003059921
        8174135966 2904357290 0334295260
        5956307381 3232862794 3490763233

(Note: The 99th-108th digits of e = 7427466391
is the first 10-digit prime in consecutive digits of e.
This is the answer to the Google Billboard question
that may lead to a job opportunity at,
(San Jose Mercury News, 7-10-2004)

How to find the answer:

My 15-year old niece Emily asked me whether I knew
the first 10-digit prime in consecutive digits of e.
She found the question in today's San Jose Mercury News,
and said if I knew the answer, it may lead to a job at Google.
I told her that one needs to examine 10-digits sequentially in
e = 2.71828182845904523536... to see if they can be
factored. If not, then it's a prime number.

Data on the e may be found at
1000 digits of e and First 1000 digits of e.
The web site Prime Curios! lists
97 primes with 10-digits.
But none of them were associated with e.
Using Dario Alpern's Test for Primes, and ignoring
10-digits which end in even numbers or 0 & 5,
the first 10-digit prime candidate in e, 8281828459
had factors of 383 x 4129 x 5237.
The next candidate 2845904523 had
factors of 3 x 7 x 11 x 103 x 119611.
Proceeding in this manner, we find
the first 10-digit prime at the
99th-108th digits of e = 7427466391.

A Google billboard on Hwy. 101 in Belmont
challenges wanna-be employees to solve
an equation that ultimately takes them
to a company jobs Web site.

Learn more about Prime Numbers & e

When you go to
there is a series of numbers:

f(1) = 7182818284
f(2) = 8182845904
f(3) = 8747135266
f(4) = 7427466391
f(5) = __________

Can you find a pattern?
Clue: add the 10-digits in
f(1), f(2), f(3), f(4)...

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© Peter Y. Chou,
P.O. Box 390707, Mountain View, CA 94039
email: (7-10-2004)