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# Prime or composite?

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Can you determine whether this number which has 7 elevens and 11 sevens is a Prime or Composite number?     11 11 11 11 11 11 11 7 7 7 7 7 7 7 7 7 7 7. Thanks.

Guest Feb 20, 2017

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ok so i checked an online prime number checker and it said it is prime

Scruffy23.  Feb 20, 2017
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well, to work out if 1,111,111,111,111,177,777,777,777 is a prime number, we find the square root of it and round it up (so if you have 11.3 round it up to 12) then see if any primes below that number divide into it (i have a bad feeling about this). sqrt(1,111,111,111,111,177,777,777,777)=1054092553389.491 rounded up is 1054092553390. Then i give up and let my brain solidify again and take a nap

Scruffy23.  Feb 20, 2017
#3
+246
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ok so i checked an online prime number checker and it said it is prime

Scruffy23.  Feb 20, 2017
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Using Miller–Rabin primality test, it shows that  11 11 11 11 11 11 11 7 7 7 7 7 7 7 7 7 7 7 is a PRIME number!. It can also be written as the SUM of two squares as follows:

n = a² + b²

a = 1,053,802,513,824

b = 24,725,957,401

Guest Feb 20, 2017