What are 2 prime numbers that when multiplied together generates a 400-digit number.?

I tried for a day now and I cant come up with the solution. Please help. What was your strategy?


Thanks.What are 2 prime numbers that when multiplied together generates a 400-digit number.?
10^14 - 29 is a 14-digit prime.


2^1279 - 1 is a 386-digit Mersenne prime.


Their product is:


1040793219466138078


1588787651630327218


920326662460506379


26740500601006


551709174325167


493416724590063


540431923994067


670552333682475


6063963673


927892800853960


190008483086367


9723482154604757


613093273015575613180526


529797348471022


970877005897123


255668411663308


617898265584473


6167634838


7979463856566


6377655655966


4581985575060


4871242259524


7376352154825


86318


3119078122659


624972163544


9589972302584


608106856477


which, as you can readily count, has 400 digits!


If you can find a prime with 399 digits, you can probably just multiply it by 2 or 11.What are 2 prime numbers that when multiplied together generates a 400-digit number.?
When multiplying two numbers you simply add the number of digits the two numbers have together (with single digits and numbers where the first 2 numbers multiple to a single digit as exceptions) to find out the number of digits the product will have. Just look for two numbers that are prime and add to 400 ~ 401 digits depending on whether or not the first 2 numbers multiply to a single or double digit number.





E.g.


58021664585639791181184025950440248398鈥?





%26amp;





29072553456409183479268752003825253455鈥?br>




Read: Source.
The highest and lowest 400-digit numbers are 10^400 and 10^401-1 respectively. Any two (whole) numbers between their square roots, 10^200 and approx. 3.162*10^200 respectively, will have a product with 400 digits. (It will not work with just any two 200-digit primes!)





Now all you have to do is find two primes that fall in between those two numbers. Looking for primes this big by hand takes months if not years, and one of your factors will have at least 200 digits, no matter what the other one is. I'd suggest using a computer to generate the primes or simply read them off a list.





Example:





290725534564091834792687520038


252534556728392227894452232349


151156829219216211827141646840


487198910591497633529398886290


016527682869989322240009808611


277510978863644323070052837841


55195197202827350411





and





126546462199632674052988251045


511424502130384205667982084173


932915673143798317892591732335


068110837745271839539998626752


392921851311786713170610204444


907332875883839187930956084100


78925861028249824377





have a 400-digit product.
try [( 3*10^20)+1][(3*10^16)+1]


or


[m!+1][n!+1]


or something of this type!
any 200-digit number
Hmm, how could the product of two numbers be prime? Only way I can think is if one of them equals 1, but 1 is not a prime.