Prime Number Challenge!

An integer greater than one is called a prime number if its only positive divisors (factors) are one and itself.

Here is a chart detailing the all Primes from 1 - 100

We know via the proof-by-contradiction by Euclid that there are an infinite number of prime numbers, yet, this doesn't reveal them. Unlike a standard integer (whereupon whatever number you can come up with, for example n, i can surpass this number with the simple exercise of n+1), large prime numbers are incredible difficult to find. There is no formula for churning out prime numbers, they must be found :)

In 2008, a mathematician won $100,000 for finding the next highest prime number (the largest known to date)

The number is 2^43112609-1

Most likely you students won't be able to grasp how big this number really is, but, for intents and purposes, if you were to sum up all the atoms in the entire universe you would get a number roughly  10^80 (vastly smaller than the one shown here)

If you would like to see how big this number really is i suggest you download it from here http://prime.isthe.com/chongo/tech/math/prime/m43112609/prime-c.html 

I will produce a tiny fraction of the full number for you here, but if you want the full thing, you must go to the prime site http://prime.isthe.com/chongo/tech/math/prime/m43112609/prime.html

three hundred sixteen quattuormilliamilliatrecensexviginmilliaunsexagintillion,
four hundred seventy quattuormilliamilliatrecensexviginmilliasexagintillion,
two hundred sixty nine quattuormilliamilliatrecensexviginmillianovemquinquagintillion,
three hundred thirty quattuormilliamilliatrecensexviginmilliaoctoquinquagintillion,
two hundred fifty five quattuormilliamilliatrecensexviginmilliaseptenquinquagintillion,
nine hundred twenty three quattuormilliamilliatrecensexviginmilliasexquinquagintillion,
one hundred forty three quattuormilliamilliatrecensexviginmilliaquinquinquagintillion,
four hundred fifty three quattuormilliamilliatrecensexviginmilliaquattuorquinquagintillion,
seven hundred twenty three quattuormilliamilliatrecensexviginmilliatrequinquagintillion,
nine hundred forty nine quattuormilliamilliatrecensexviginmilliadoquinquagintillion,
three hundred thirty seven quattuormilliamilliatrecensexviginmilliaunquinquagintillion,
five hundred sixteen quattuormilliamilliatrecensexviginmilliaquinquagintillion,
fifty four quattuormilliamilliatrecensexviginmillianovemquadragintillion,
one hundred six quattuormilliamilliatrecensexviginmilliaoctoquadragintillion,
one hundred eighty eight quattuormilliamilliatrecensexviginmilliaseptenquadragintillion,
four hundred seventy five quattuormilliamilliatrecensexviginmilliasexquadragintillion,
two hundred sixty four quattuormilliamilliatrecensexviginmilliaquinquadragintillion,
six hundred forty four quattuormilliamilliatrecensexviginmilliaquattuorquadragintillion,
one hundred forty quattuormilliamilliatrecensexviginmilliatrequadragintillion,
three hundred four quattuormilliamilliatrecensexviginmilliadoquadragintillion,
one hundred seventy six quattuormilliamilliatrecensexviginmilliaunquadragintillion,
seven hundred thirty two quattuormilliamilliatrecensexviginmilliaquadragintillion,
eight hundred eleven quattuormilliamilliatrecensexviginmillianovemtrigintillion,
two hundred forty seven quattuormilliamilliatrecensexviginmilliaoctotrigintillion,
four hundred ninety three quattuormilliamilliatrecensexviginmilliaseptentrigintillion,
sixty nine quattuormilliamilliatrecensexviginmilliasextrigintillion,
three hundred sixty eight quattuormilliamilliatrecensexviginmilliaquintrigintillion,
six hundred ninety two quattuormilliamilliatrecensexviginmilliaquattuortrigintillion,
forty three quattuormilliamilliatrecensexviginmilliatretrigintillion,
one hundred eighty five quattuormilliamilliatrecensexviginmilliadotrigintillion,
one hundred twenty one quattuormilliamilliatrecensexviginmilliauntrigintillion,
six hundred eleven quattuormilliamilliatrecensexviginmilliatrigintillion,
eight hundred thirty seven quattuormilliamilliatrecensexviginmillianovemvigintillion,
eight hundred fifty six quattuormilliamilliatrecensexviginmilliaoctovigintillion,
seven hundred twenty six quattuormilliamilliatrecensexviginmilliaseptenvigintillion,
eight hundred sixteen quattuormilliamilliatrecensexviginmilliasexvigintillion,
five hundred thirty nine quattuormilliamilliatrecensexviginmilliaquinvigintillion,
nine hundred eighty five quattuormilliamilliatrecensexviginmilliaquattuorvigintillion,
four hundred sixty five quattuormilliamilliatrecensexviginmilliatrevigintillion,
ninety seven quattuormilliamilliatrecensexviginmilliadovigintillion,
three hundred fifty six quattuormilliamilliatrecensexviginmilliaunvigintillion,
one hundred twenty three quattuormilliamilliatrecensexviginmilliavigintillion,
four hundred thirty two quattuormilliamilliatrecensexviginmillianovemdecillion,
six hundred forty five quattuormilliamilliatrecensexviginmilliaoctodecillion,
one hundred seventy nine quattuormilliamilliatrecensexviginmilliaseptendecillion,
six hundred seventy three quattuormilliamilliatrecensexviginmilliasexdecillion,
eight hundred fifty three quattuormilliamilliatrecensexviginmilliaquindecillion,
five hundred ninety quattuormilliamilliatrecensexviginmilliaquattuordecillion,
five hundred seventy seven quattuormilliamilliatrecensexviginmilliatredecillion,
two hundred thirty eight quattuormilliamilliatrecensexviginmilliadodecillion,
one hundred seventy nine quattuormilliamilliatrecensexviginmilliaundecillion,
three hundred fifty seven quattuormilliamilliatrecensexviginmilliadecillion,
nine hundred quattuormilliamilliatrecensexviginmillianovemtillion,
eight hundred seventy six quattuormilliamilliatrecensexviginmilliaoctotillion,
four hundred twenty six quattuormilliamilliatrecensexviginmilliaseptentillion,
one hundred three quattuormilliamilliatrecensexviginmilliasextillion,
nine hundred forty three quattuormilliamilliatrecensexviginmilliaquintillion,
seven hundred eighty two quattuormilliamilliatrecensexviginmilliaquattuortillion,
three hundred seventy six quattuormilliamilliatrecensexviginmilliatretillion,
four hundred ninety four quattuormilliamilliatrecensexviginmilliadotillion,
five hundred ninety one quattuormilliamilliatrecensexviginmilliauntillion,
seven hundred forty two quattuormilliamilliatrecensexviginmilliatillion,
nine hundred thirty four quattuormilliamilliatrecenquinviginmillianongennovemnonagintillion,
five hundred eighty eight quattuormilliamilliatrecenquinviginmillianongenoctononagintillion,
four hundred ninety seven quattuormilliamilliatrecenquinviginmillianongenseptennonagintillion,
one hundred seventeen quattuormilliamilliatrecenquinviginmillianongensexnonagintillion,
five hundred eighty seven quattuormilliamilliatrecenquinviginmillianongenquinnonagintillion,
one hundred forty six quattuormilliamilliatrecenquinviginmillianongenquattuornonagintillion,
nine hundred sixteen quattuormilliamilliatrecenquinviginmillianongentrenonagintillion,
nine hundred seventy two quattuormilliamilliatrecenquinviginmillianongendononagintillion,
nine hundred eighty four quattuormilliamilliatrecenquinviginmillianongenunnonagintillion,
seven hundred sixty one quattuormilliamilliatrecenquinviginmillianongennonagintillion,
one hundred fifty nine quattuormilliamilliatrecenquinviginmillianongennovemoctogintillion,
sixty quattuormilliamilliatrecenquinviginmillianongenoctooctogintillion,
eight hundred seventy three quattuormilliamilliatrecenquinviginmillianongenseptenoctogintillion,
two hundred fifty quattuormilliamilliatrecenquinviginmillianongensexoctogintillion,
nine hundred thirty nine quattuormilliamilliatrecenquinviginmillianongenquinoctogintillion,
four hundred sixty two quattuormilliamilliatrecenquinviginmillianongenquattuoroctogintillion,
eighty five quattuormilliamilliatrecenquinviginmillianongentreoctogintillion,
five hundred seventy five quattuormilliamilliatrecenquinviginmillianongendooctogintillion,
seven hundred forty quattuormilliamilliatrecenquinviginmillianongenunoctogintillion,
seven hundred fifty four quattuormilliamilliatrecenquinviginmillianongenoctogintillion,
five hundred seventy seven quattuormilliamilliatrecenquinviginmillianongennovemseptuagintillion,
ninety eight quattuormilliamilliatrecenquinviginmillianongenoctoseptuagintillion,
six hundred twenty quattuormilliamilliatrecenquinviginmillianongenseptenseptuagintillion,
five hundred fifty eight quattuormilliamilliatrecenquinviginmillianongensexseptuagintillion,
eleven quattuormilliamilliatrecenquinviginmillianongenquinseptuagintillion,
seven hundred seventy nine quattuormilliamilliatrecenquinviginmillianongenquattuorseptuagintillion,
five hundred twenty nine quattuormilliamilliatrecenquinviginmillianongentreseptuagintillion,
eight hundred eighty four quattuormilliamilliatrecenquinviginmillianongendoseptuagintillion,
forty two quattuormilliamilliatrecenquinviginmillianongenunseptuagintillion,
one hundred ninety eight quattuormilliamilliatrecenquinviginmillianongenseptuagintillion,
two hundred eighty seven quattuormilliamilliatrecenquinviginmillianongennovemsexagintillion,
six hundred forty three quattuormilliamilliatrecenquinviginmillianongenoctosexagintillion,
three hundred nineteen quattuormilliamilliatrecenquinviginmillianongenseptensexagintillion,
three hundred thirty quattuormilliamilliatrecenquinviginmillianongensexsexagintillion,
four hundred sixty five quattuormilliamilliatrecenquinviginmillianongenquinsexagintillion,
sixty four quattuormilliamilliatrecenquinviginmillianongenquattuorsexagintillion,
four hundred fifty five quattuormilliamilliatrecenquinviginmillianongentresexagintillion,
two hundred thirty four quattuormilliamilliatrecenquinviginmillianongendosexagintillion,
nine hundred eighty eight quattuormilliamilliatrecenquinviginmillianongenunsexagintillion,
one hundred forty two quattuormilliamilliatrecenquinviginmillianongensexagintillion,
one hundred thirty nine quattuormilliamilliatrecenquinviginmillianongennovemquinquagintillion,
five hundred sixty five quattuormilliamilliatrecenquinviginmillianongenoctoquinquagintillion,
seven hundred eighty five quattuormilliamilliatrecenquinviginmillianongenseptenquinquagintillion,
four hundred forty seven quattuormilliamilliatrecenquinviginmillianongensexquinquagintillion,
four hundred seventy four quattuormilliamilliatrecenquinviginmillianongenquinquinquagintillion,
twenty three quattuormilliamilliatrecenquinviginmillianongenquattuorquinquagintillion,
five hundred forty six quattuormilliamilliatrecenquinviginmillianongentrequinquagintillion,
three hundred fifty three quattuormilliamilliatrecenquinviginmillianongendoquinquagintillion,
seven hundred fifty eight quattuormilliamilliatrecenquinviginmillianongenunquinquagintillion,
five hundred thirty seven quattuormilliamilliatrecenquinviginmillianongenquinquagintillion,
three hundred twenty four quattuormilliamilliatrecenquinviginmillianongennovemquadragintillion,
eight hundred one quattuormilliamilliatrecenquinviginmillianongenoctoquadragintillion,
eight hundred thirty eight quattuormilliamilliatrecenquinviginmillianongenseptenquadragintillion,
one hundred twenty quattuormilliamilliatrecenquinviginmillianongensexquadragintillion,
three hundred eighty seven quattuormilliamilliatrecenquinviginmillianongenquinquadragintillion,
six hundred quattuormilliamilliatrecenquinviginmillianongenquattuorquadragintillion,
eight hundred sixty eight quattuormilliamilliatrecenquinviginmillianongentrequadragintillion,
four hundred sixteen quattuormilliamilliatrecenquinviginmillianongendoquadragintillion,
five hundred twenty five quattuormilliamilliatrecenquinviginmillianongenunquadragintillion,
four hundred quattuormilliamilliatrecenquinviginmillianongenquadragintillion,
seven hundred ninety quattuormilliamilliatrecenquinviginmillianongennovemtrigintillion,
three hundred eighty one quattuormilliamilliatrecenquinviginmillianongenoctotrigintillion,
two hundred eighty five quattuormilliamilliatrecenquinviginmillianongenseptentrigintillion,
eight hundred eighty eight quattuormilliamilliatrecenquinviginmillianongensextrigintillion,
two hundred fifty six quattuormilliamilliatrecenquinviginmillianongenquintrigintillion,
six hundred eighty seven quattuormilliamilliatrecenquinviginmillianongenquattuortrigintillion,
eighty five quattuormilliamilliatrecenquinviginmillianongentretrigintillion,
eight hundred fifty five quattuormilliamilliatrecenquinviginmillianongendotrigintillion,
four hundred fifty six quattuormilliamilliatrecenquinviginmillianongenuntrigintillion,
two hundred thirty one quattuormilliamilliatrecenquinviginmillianongentrigintillion,
five hundred seventy seven quattuormilliamilliatrecenquinviginmillianongennovemvigintillion,
five hundred twenty seven quattuormilliamilliatrecenquinviginmillianongenoctovigintillion,
nine hundred thirty nine quattuormilliamilliatrecenquinviginmillianongenseptenvigintillion,
three hundred five quattuormilliamilliatrecenquinviginmillianongensexvigintillion,
nine hundred twenty quattuormilliamilliatrecenquinviginmillianongenquinvigintillion,
eight hundred eleven quattuormilliamilliatrecenquinviginmillianongenquattuorvigintillion,
seven hundred sixty six quattuormilliamilliatrecenquinviginmillianongentrevigintillion,
five hundred eighty five quattuormilliamilliatrecenquinviginmillianongendovigintillion,
three hundred eight quattuormilliamilliatrecenquinviginmillianongenunvigintillion,
six hundred seventy quattuormilliamilliatrecenquinviginmillianongenvigintillion,
one hundred thirty two quattuormilliamilliatrecenquinviginmillianongennovemdecillion,
one hundred twenty nine quattuormilliamilliatrecenquinviginmillianongenoctodecillion,
one hundred fifty five quattuormilliamilliatrecenquinviginmillianongenseptendecillion,
two hundred twenty one quattuormilliamilliatrecenquinviginmillianongensexdecillion,
eight hundred four quattuormilliamilliatrecenquinviginmillianongenquindecillion,
three hundred eighty one quattuormilliamilliatrecenquinviginmillianongenquattuordecillion,
five hundred forty eight quattuormilliamilliatrecenquinviginmillianongentredecillion,
six hundred twenty five quattuormilliamilliatrecenquinviginmillianongendodecillion,
seven hundred eighty seven quattuormilliamilliatrecenquinviginmillianongenundecillion,
nine hundred forty three quattuormilliamilliatrecenquinviginmillianongendecillion,
twenty quattuormilliamilliatrecenquinviginmillianongennovemtillion,
six hundred ninety four quattuormilliamilliatrecenquinviginmillianongenoctotillion,
five hundred twenty eight quattuormilliamilliatrecenquinviginmillianongenseptentillion,
fifteen quattuormilliamilliatrecenquinviginmillianongensextillion,
nine hundred ninety nine quattuormilliamilliatrecenquinviginmillianongenquintillion,
two hundred twenty one quattuormilliamilliatrecenquinviginmillianongenquattuortillion,
seven hundred eighteen quattuormilliamilliatrecenquinviginmillianongentretillion,
one hundred ninety one quattuormilliamilliatrecenquinviginmillianongendotillion,
five hundred fifty seven quattuormilliamilliatrecenquinviginmillianongenuntillion,
seven hundred sixty one quattuormilliamilliatrecenquinviginmillianongentillion,
seven hundred eighty nine quattuormilliamilliatrecenquinviginmilliaoctingennovemnonagintillion,
thirty eight quattuormilliamilliatrecenquinviginmilliaoctingenoctononagintillion,
five hundred thirty nine quattuormilliamilliatrecenquinviginmilliaoctingenseptennonagintillion,
five hundred twenty two quattuormilliamilliatrecenquinviginmilliaoctingensexnonagintillion,
three hundred forty nine quattuormilliamilliatrecenquinviginmilliaoctingenquinnonagintillion,
seven hundred forty six quattuormilliamilliatrecenquinviginmilliaoctingenquattuornonagintillion,
eight hundred eight quattuormilliamilliatrecenquinviginmilliaoctingentrenonagintillion,
seven hundred ninety seven quattuormilliamilliatrecenquinviginmilliaoctingendononagintillion,
four hundred seventy six quattuormilliamilliatrecenquinviginmilliaoctingenunnonagintillion,
nine hundred seven quattuormilliamilliatrecenquinviginmilliaoctingennonagintillion,
six hundred sixty four quattuormilliamilliatrecenquinviginmilliaoctingennovemoctogintillion,
fifty quattuormilliamilliatrecenquinviginmilliaoctingenoctooctogintillion,
six hundred one quattuormilliamilliatrecenquinviginmilliaoctingenseptenoctogintillion,
two hundred forty eight quattuormilliamilliatrecenquinviginmilliaoctingensexoctogintillion,
four hundred seventy three quattuormilliamilliatrecenquinviginmilliaoctingenquinoctogintillion,
two hundred six quattuormilliamilliatrecenquinviginmilliaoctingenquattuoroctogintillion,
eight hundred seventy four quattuormilliamilliatrecenquinviginmilliaoctingentreoctogintillion,
one hundred thirty three quattuormilliamilliatrecenquinviginmilliaoctingendooctogintillion,
one hundred ninety four quattuormilliamilliatrecenquinviginmilliaoctingenunoctogintillion,
six hundred sixty three quattuormilliamilliatrecenquinviginmilliaoctingenoctogintillion,
five hundred eighty five quattuormilliamilliatrecenquinviginmilliaoctingennovemseptuagintillion,
three hundred thirty four quattuormilliamilliatrecenquinviginmilliaoctingenoctoseptuagintillion,
nine hundred eighty three quattuormilliamilliatrecenquinviginmilliaoctingenseptenseptuagintillion,
eight hundred five quattuormilliamilliatrecenquinviginmilliaoctingensexseptuagintillion,
seven hundred thirty four quattuormilliamilliatrecenquinviginmilliaoctingenquinseptuagintillion,
eight hundred three quattuormilliamilliatrecenquinviginmilliaoctingenquattuorseptuagintillion,
six hundred twenty quattuormilliamilliatrecenquinviginmilliaoctingentreseptuagintillion,
seven hundred five quattuormilliamilliatrecenquinviginmilliaoctingendoseptuagintillion,
seven hundred seventy eight quattuormilliamilliatrecenquinviginmilliaoctingenunseptuagintillion,
two hundred seventy quattuormilliamilliatrecenquinviginmilliaoctingenseptuagintillion,
nine hundred ten quattuormilliamilliatrecenquinviginmilliaoctingennovemsexagintillion,
five hundred sixty one quattuormilliamilliatrecenquinviginmilliaoctingenoctosexagintillion,
seven hundred sixteen quattuormilliamilliatrecenquinviginmilliaoctingenseptensexagintillion,
seven hundred sixty seven quattuormilliamilliatrecenquinviginmilliaoctingensexsexagintillion,
six hundred eighty quattuormilliamilliatrecenquinviginmilliaoctingenquinsexagintillion,
nine hundred fifty four quattuormilliamilliatrecenquinviginmilliaoctingenquattuorsexagintillion,
eight hundred fourteen quattuormilliamilliatrecenquinviginmilliaoctingentresexagintillion,
four hundred fifteen quattuormilliamilliatrecenquinviginmilliaoctingendosexagintillion, 

BUT, with all that (using about 150 lines) there were over  4,321,381 lines omitted ...

What a mouth full!!!!

So, here is the goal. Using a large fake check made out for $100,000 and a small bag of candy, pose the challenge to see who can come up with the largest prime number using only paper, pencil and calculator (don't let them cheat on their cell phones by Googling)