73 -> 2n+1 ever prime?

[David Broadhurst]

> a=73;a=2*a+1;n=1;While[!PrimeQ[a],a=2*a+1;n++];Print[n,"   ",a], I found at
> the 2552rd iteration the Probable Prime listed below.
 
Nexy, at the 4892nd iteration,

a[4892]

= 3220850062345993214287069881613280515446590907525498112334746745575042\
946080393855946358261105652186984603752555040067109719792892010495196135\
734143486206044048783346523155748840514745091030349541363263867600350019\
664862870843469259067830869530442808073309234314395828197653981244629899\
304928057361812370849055011538640000559879700863356681741196213555424266\
281432381028862003733174659921930865142580957719394364180138575710877104\
197632412794187530070953985536213886182504578766886524953522812877078083\
102502457272124973228960871866704463275820492009212145689545731277583088\
494319398679115341402625753985665855475179392437107726242770531565030511\
231249919872620471342289642956636024328940025390601394847926280096234744\
892846000390864875967224248480641689614561755309716262314448594522984881\
613660219473847869212471586261805013660737861861320566454965510103082682\
538366345984833276705714138804006881735988521385688976663041860462840255\
555517553476386248159687992034137767158379805658984667824882662322912462\
621281296490575900857692277734857351238628198947739781026635832283282332\
749812291177829219754437239448000418615679427716839801058694606877772974\
594284580445251418552019805196761083510472706501615421301989562817210465\
497949014281607060306021338714181675910144587225558810573495100703572869\
949589117446445660607462891932946042889757404896218863979627961894507732\
169247695419516615357141851146123076565161335684803789888511251568663153\
7555850824012727622369632578965602303

is probably prime

So here is a funny sequence:

description:
n>0 such that a[n]=2*a[n-1]+1 is probably prime with a[0]=73


             2252, 4892, ????

I think that this qualifies as "hard" ?

David Broadhurst