Some factorization problems (and solutions)

Long strings of zeros and nines compress well.

g= [10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 22, 23, 25, 27, 29, 32, 34, 37, 40, 43, 46, 50, 54, 58, 63, 68, 74, 79, 86, 93 ] ; for(i=1, 307, for(j=1, 30, s=(g[j]*10^i); a=precprime(s); b=nextprime(2*s); c=a*b; lc=log(c); print(ceil(lc/log(2)), " ", ceil(lc/log(10)), " ", c, " ", g[j], "*10^", i, a-s)))