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Old 2016-03-19, 06:06   #1
PawnProver44
 
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"NOT A TROLL"
Mar 2016
California

197 Posts
Post Is there a prime of the form......

Is there a prime for every power of 3 just by adding 1 to a single digit. In other words, is there always a prime of the form 3^x+10^y for y ≤ x. (I found this to be false, More generally, is there a prime of the form a^x+b^y for fixed a, x, and b if a and b are coprime. For the example 3^x+10^y, I found this to be true for all x values less than 100:

3^1+10^1 is prime (13)
3^2+10^1 is prime (19)
3^3+10^1 is prime (37)
3^4+10^2 is prime (181)
3^5+10^4 is prime (10243)
3^6+10^1 is prime (739)
3^7+10^2 is prime (2287)
3^8+10^1 is prime (6571)
3^9+10^4 is prime (29683)
3^10+10^2 is prime (59149)
3^11+10^6 is prime (1177147)
3^12+10^8 is prime (100531441)
3^13+10^3 is prime (1595323)
3^14+10^6 is prime (5782969)
3^15+10^y is composite for y ≤ 15.

I tested x < 100

Any other known values of x such that this is true?
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