The night sky we see as a random scattering of stars is an aspect of the order of galaxies. Primes, scattered through the whole numbers, are patterns superimposed on patterns, obscured by multiplicity like the faint path of the Milky Way.
 

Can this pattern be used to generate large primes?
In general, mathematicians are unconcerned with palindromes and string-type readings of numbers. However, it is relatively simple to convert a number to another base. Since the bands of prime intensity are in regular areas, it's possible to use trigonometry to find the bases to convert to (since you know the length and adjacent angle.) This doesn't guarantee the new number generated will be prime, but makes it more likely. But while the new number may be prime, it may not be a larger prime than the original.

Are primes numbers and fractals related?
There is some work suggesting that primes have the property of self similarity.

Another similarity lies in creation by iteration. In the sieve of Eratosthenes, each successive iteration removes a group of multiples. While these iterations are not strictly identical, since each group of multiples is spaced further apart along the number line, each group of multiples is an orderly pattern. And yet, as a new pattern is overlaid at each orderly iteration, the result appears more complex, even chaotic.

The Primes and Beyond
"In 1974, the most powerful broadcast ever deliberately beamed into space was made from Puerto Rico. The broadcast formed part of the ceremonies held to mark a major upgrade to the Arecibo Radio Telescope. The transmission consisted of a simple, pictorial message..."
(An image of the SETI message sent to M13 encoded with primes.)

Clarke and the Primes
"Jeserac sat motionless within a whirlpool of numbers. The first thousand primes..."

Arthur C. Clarke wrote about the glamor of primes in his novel, The City and the Stars. His description anticipates the prime spiral discovered by Ulam. See the Mathworld link above for a description and the complete quote.