You can always make sieve file for that sequence

305531329 | 21181*2^34279700+1
305676377 | 21181*2^34275572+1
306369697 | 21181*2^34160204+1
306388063 | 21181*2^38718308+1
306603233 | 21181*2^39168980+1
306633857 | 21181*2^37296188+1
306641417 | 21181*2^38552204+1
306928913 | 21181*2^32814500+1
306991679 | 21181*2^32759852+1
307224371 | 21181*2^38975372+1
307264571 | 21181*2^33503108+1
307375631 | 21181*2^35924972+1
307459249 | 21181*2^32029124+1
307628603 | 21181*2^38360780+1
308280677 | 21181*2^33951524+1
308339789 | 21181*2^32662604+1
308450627 | 21181*2^31753412+1
308844059 | 21181*2^33154412+1
308844127 | 21181*2^32154164+1
308903227 | 21181*2^38121572+1
309236093 | 21181*2^34932980+1
309245621 | 21181*2^32854868+1
309435257 | 21181*2^32242412+1
____________
92*10^^1585996-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^⁴⁹⁸¹⁰¹-1 CRUS PRIME
2022202116^¹³¹⁰⁷²+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie!