So i got a number with 4033 Digits (101010...0101) Is there anyway

>>7694485
divide it by every number lower than half of it and see if you get a whole number.

>>7694497
that would take a really long time.
also to the squareroot of it is enough

>>7694485
AKS Primality Test

>>7694926
OP here
i am sorry that the question wasnt totally clear
i just Need to proof it mathematically i dont Need to calculate the solution nor am i allowed to use a program for it

>>7694485
Only numbers whose last digits are 1, 3 or 7 can multiply and equal a numerical value with the last digit 1. Fuck 7 x 43 = 301 nvm op. I'd thought it was impossible for any number multiplied by 7, 3 or 1 to end in 01. :(

>>7695010
9 too...Let's....just forget I said anything. n_n

>>7695010
well dude 9 * 89 equals 801
but thanks for the effort

>>7694485
Take away one, multiply the number by two, take away the original number and add two. Now, if two DOES NOT divide your number, then your original number MIGHT be a prime.

>>7695027
But wait all values which can be multiplied to end in 1 always contain a disparate digit-value from 0 and 1 sans for numerical values ending in one itself. Hm.

>>7694505
Use those cool new computer things .

>>7695029
well how about you write down the number you calculate with this ?
also please the steps
i am very courious

>>7695036
Alright just figured out that it's gonna be 100...01 x 101. Try the proof that all 100...01 values x 101 always end as 1010101...01

>>7695046
Incorrect. On the right track.

>>7695046
thats a nice concept
thanks alot
just if you wanna know i tried it about the Digit sum all the way up to the 100th alternating Digit sum

>>7695046
>>7695052
allright got it
10001 * 101 = 1010101
1000001 * 10101 = 10101010101
or generally speaking
you can multiply a string of 1000...0001
with a string which lenght equals the amount of Zeros in the first one 101010..101 and the result is a string 1010..10101 with the combined lenght of the first two strings -1

thanks alot anon for this concept

OP here yet again
i am stupid this>>7695063
only works for even amounts of 1 for the second string
but for my Problem there are a total of 2017 1`s and 2016 0´s
so yeah Problem still stands

>>7694485
Please update when you get it, pretty interested in this (and primes in general)

>>7695147
ok i actually got it
so a * b = c
for c>1 and amount of the Digit 1in c = uneven
a is c with the 0 left out
(for example c= 10101 ; a = 111
c = 101010101; a = 11111 etc)

so for b you take the amount of 0 in c
thats your lenght of b
first you put an 1 on the end of b then you fill the rest alternating with 0 and 9 with priority on 9 for the first one
(example: c = 10101 ; b = 91
c = 101010101 ; b= 9091)

that solves it

>>7695063
HAHA SUHWEET! I went to go pick up my car and figured out the EXACT same thing. I was going to word it as "For however many digits contained within a number following the pattern 1010...10101, insert that same amount of digits in the form of zeroes between a number following the pattern 1...1." You got this OP. Good luck.

>>7695187
thanks and i got to thank you you brought me to this concept

>>77695187
You're right about the (# of digits from first number) + (# of digits from second number) - 1 = (# of digits in the product) though.

>>7695210
*Salute*

>>7694485
Do you mean decimal or binary?

You can use the Fermat test though. Testing everything up to the squareroot of that will take ages.

>>7695227
decimal
and i solved it here>>7695174
using fermat would take ages:
n is my number; a >1 and a<=n-1
a^n Euclidean Division(n) = 0
if this is true then n is not an prime
but since n is a number with 4033 Digits even choosing the smallest a would be 2^(number with 4033 Digits)
this would simply take way too long

>>7695241
Yeah realized that after posting. It's 4AM here.

well 0.30 am for me and i still have to write it down
thanks for everyone who was helping
cya

>>7695043
Start with x. Take away one to get a new number y. Multiply by two so you get a new number z. Take away original to get a, add two to get b.

Make a program to find if a number is prime.