Letters associated with prime numbers
Python 3,262 236 209 196 179 114 93 92  97 bytes



def f(n):
 m=k=1;s=''
 while n:m*=k*k;k+=1;n-=m%k
 while k:s=chr(~-k%26+97)+s;k=~-k//26
 return s


Try it online!

Fixed a bug mentioned by @benrg about getting a wrong output for the input 123.

Thanks to:
- @AdmBorkBork for help me getting started and save a few bytes
- @Sriotchilism O'Zaic for saving me 6 bytes
- @mypetlion for saving me 65 bytes and bringing me under 150 bytes :)
- @dingledooper for saving me 21 bytes and bringing me under 100 bytes :D
- @Jitse for saving 1 byte  



98 bytes



f=lambda n,i=1,p=1:n and-~f(n-p%i,i+1,p*i*i)
g=lambda n,s='':n and g(~-n//26,chr(~-n%26+97)+s)or s


Try it online!