- I agree with Phil.

Calculate 3^53,106 -> 3

then 2^3+99 = 107 , 107 =0 mod 107

best

--- Phil Carmody <thefatphil@...> schrieb am Di, 9.6.2009:

Von: Phil Carmody <thefatphil@...>

Betreff: Re: [PrimeNumbers] Too big for any computer?

An: "Prime Number" <primenumbers@yahoogroups.com>

Datum: Dienstag, 9. Juni 2009, 16:37

--- On Tue, 6/9/09, Devaraj Kandadai <dkandadai@gmail. com> wrote:

> I had requested Ken (Kradenken) to test whether 2^(3^53) + 99 is

> eactly divisible by 107 or not. He replied that

> the number is too big for any computer. Do you agree?

If by "the number" you mean 2^(3^53)+99, then clearly it isn't too big for any computer as it can trivially be represented using only 9 characters. It's binary or decimal expansion is too big, but no-one's asking for its binary or decimal expansion, so that's irrelevant.

To test whether it's divisible by 107 is trivial also, as 2^phi(107) == 1 (mod 107). So reduce 3^53 modulo phi(107):

? Mod(2,107)^lift( Mod(3,eulerphi( 107))^53) +99

Mod(0, 107)

So indeed, it is divisible by 107.

Phil

[Non-text portions of this message have been removed] - Devaraj Kandadai wrote:
> I had requested Ken (Kradenken) to test whether 2^(3^53) + 99 is

If you represent the numbers directly, then, yes, it's too big for

> eactly divisible by 107 or not. He replied that the number is too big for

> any computer. Do you agree?

any computer. However, I gave you a very short program the other day

that shows a very simple way to test factors of large numbers like this

using modular arithmetic. It could be trivially modified to answer this

question, and test any number of factors that you chose for this or any

of the other numbers that you've been asking about. I would suggest

that you study it again, because it would help you answer repeated

questions of this sort, and it would become a useful tool in your studies.

Again, a suitable Frink program to exhaustively list the factors of

your number is below: ( http://futureboy.us/frinkdocs/ ) If you have a

recent version of Java installed, Frink is a one-click install from

http://futureboy.us/frinkjar/frink.jnlp .

Switch to programming mode (control-P) and paste in the following

program. Hint: modPow[n,e,base] does (n^e) mod base, but does it

efficiently without the numbers getting larger than base. Other

languages should have a similar function, too, if you'd like to

implement this in another language. You will be able to answer these

and future similar questions easily if you understand how this program

works.

-------------------------------------------------

e = 3^53

n = 1

while true

{

n = nextPrime[n]

if (modPow[2,e,n] + 99) mod n == 0

print[n + " "]

}

-----------------------------------------------------

--

Alan Eliasen

eliasen@...

http://futureboy.us/ - Hi All,
--- In primenumbers@yahoogroups.com, Devaraj Kandadai <dkandadai@...> wrote:

>

> I had requested Ken (Kradenken) to test whether 2^(3^53) + 99 is

> eactly divisible by 107 or not. He replied that the number is too big for

> any computer. Do you agree?

Hi All,

In defence of my statement the original request was could I use pfgw on the number (2^(3^53)+99)/107 as Deva received an overflow in Pari

I assumed a prp test was being requested.

Hence my reply

Cheers Ken - Peace All,

Is there a given name to prime numbers that have prime digit sums?

Example 67 and 6+7=13

If not can someone please suggest a short name if possible.

I really need to classify five different kinds of primes as shown below

but the above case is the most urgent one please, thank you in advance.

1) Prime with a prime digit sum

Example 67 and 6+7=13

2) Prime with a prime digit sum recusively for all subsequent sums [Recusive Primes]

Example 47, 4+7=11 and 1+1=2

3) Prime with prime digits

Example 37, 3 and 7

4) Prime with prime digits and a prime digit sum

Example 337, 3, 3, 7 and 3+3+7=13

5) Prime with prime digits and a prime digit sum recusively for all subsequent sums [Pure Primes]

Example 227, 2, 2, 7, 2+2+7=11, and 1+1=2

Thank you all in advance and the most urgent one is kind (1) please.

[Non-text portions of this message have been removed] - Maybe

Sum Of Digits Is Prime - SODIP or SODIPS for more than one.

So we have another name for "additive" primes in The Encyclopedia of Integer Sequences.

An internet search has a lot of SODIP hits.

So when you dip into the big bucket of primes if you dip just right or SODIP, you may draw

sum of your primes schooner or ladle.

Of course SODIP applies to all integers. I guess we could extend the name a little with

SODOPIP. Ohoo.. the PIP part is exciting - Prime-Index-Primes. Now if we look for SODIPS

for PIPS we have a new sequence.

Enjoy,

Suds Of Draught In Pint,

Cino

To: primenumbers@yahoogroups.com

CC: pureprimes@...

From: alipoland@...

Date: Wed, 24 Jun 2009 07:20:22 -0700

Subject: [PrimeNumbers] What is the name for this kind of primes

Peace All,

Is there a given name to prime numbers that have prime digit sums?

Example 67 and 6+7=13

If not can someone please suggest a short name if possible.

I really need to classify five different kinds of primes as shown below

but the above case is the most urgent one please, thank you in advance.

1) Prime with a prime digit sum

Example 67 and 6+7=13

2) Prime with a prime digit sum recusively for all subsequent sums [Recusive Primes]

Example 47, 4+7=11 and 1+1=2

3) Prime with prime digits

Example 37, 3 and 7

4) Prime with prime digits and a prime digit sum

Example 337, 3, 3, 7 and 3+3+7=13

5) Prime with prime digits and a prime digit sum recusively for all subsequent sums [Pure Primes]

Example 227, 2, 2, 7, 2+2+7=11, and 1+1=2

Thank you all in advance and the most urgent one is kind (1) please.

[Non-text portions of this message have been removed]

[Non-text portions of this message have been removed]