[cvogqzhd] Some large safe primes

Finding the largest safe prime less than certain powers of two:

sophie(x)=(x%6==5)&&ispseudoprime(x)&&ispseudoprime(2*x+1)
f(start)=for(d=0,start,i=start-d;print(d);if(sophie(i),return(i-start)))

I confirm 2^512 - 38117 and 2^1024 - 1093337, and add 2^1536 - 1503317 and 2^3072 - 1103717 and 2^4096 - 10895177 .

The web claims 2^2048 - 1942289, also I confirmed.

Update: 2^8192 - 43644929
Update 2: 2^16384 - 364486013

So the complete known sequence for 2^(2^i), i=2..13 is 5 29 269 209 1469 15449 36113 38117 1093337 1942289 10895177 43644929 364486013

Further work by others at OEIS A181356.

It would be nice to get solutions for exponents 6144, 12288, 24576.