Hello!

Prime numbers I found so far (all proven by N+1, N-1, or Primo):

731969*3615-1
731969*3617-1
731969*3699-1
731969*2979+1
26350885*365+1
26350885*366+1
26350885*368+1
26350885*3627+1
26350885*3648+1
26350885*3665+1
26350885*36264+1
26350885*36551+1
26350885*362009+1
26350885*362224+1
26350885*364776+1
26350885*365067+1
17944*3618-1 - Sophie Germain - 35888*3618-1
17944*36340-1
17944*361716-1
17944*362666-1
17944*362838-1
4133660484201617547*3618-1
4133660484201617547*3654-1
4133660484201617547*3696-1
4133660484201617547*364209-1
4133660484201617547*3677+1
4133660484201617547*36231+1
4133660484201617547*36882+1
4133660484201617547*361589+1
4133660484201617547*362501+1
833033*365+1
833033*3612+1
833033*36324+1
833033*36647+1
833033*361377+1
833033*364085+1
833033*365204+1
833033*367836+1
833033*3614697+1
50!/(26!*25!)+1
138!/(70!*69!)+1
172!/(87!*86!)+1
180!/(91!*90!)+1
190!/(96!*95!)+1
208!/(105!*104!)+1
290!/(146!*145!)+1
406!/(204!*203!)+1
430!/(216!*215!)+1
454!/(228!*227!)+1
582!/(292!*291!)+1
618!/(310!*309!)+1
644!/(323!*322!)+1
674!/(338!*337!)+1
814!/(408!*407!)+1
960!/(481!*480!)+1
1584!/(793!*792!)+1
1646!/(824!*823!)+1
1838!/(920!*919!)+1
2002!/(1002!*1001!)+1
2318!/(1160!*1159!)+1
4452!/(2227!*2226!)+1
5486!/(2744!*2743!)+1
5644!/(2823!*2822!)+1
8500!/(4251!*4250!)+1
16154!/(8078!*8077!)+1
16218!/(8110!*8109!)+1
32048!/(16025!*16024!)+1
RSA-2048*2164-1
RSA-2048*2226-1
RSA-2048*2834-1
RSA-2048*21732-1
RSA-2048*23920-1
RSA-2048*24176-1
RSA-2048*24220-1
RSA-2048*25756-1
RSA-2048*29250-1
RSA-2048*214832-1



Numbers I like the most (composites have factors after them):

911
9118675309
8675309
4198862272=2^6*11*5964293
4198862272127
709
907
90709
phi=1.6180339887...
pi=3.1415926535...
M911=1823*26129303*201955048939840841121786425435009*179952067635826383624911677398309377606773178810479797675552286320427397321-
42377995426697752537713012686173747568966535784452675227646966034598664601477152955273561717424308130853743953099299250987929984-
79072683867643648045147452807
M43112609
M127, MM127, MMM127, etc.

Base-36 Values of k (Star Wars aliens were the inspiration for these numbers):
731969=FOSH (a sentient alien bird species)
26350885=FOSH1 (same as above)
17944=DUG (an alien that uses it's arms as legs and vice versa, searched up to n=10000)

Other Base-36 k values I may use in the future:

VELOCIRAPTOR  (4133660484201617547=34*173*311*948513010129) (only 3 primes for n<1000, still searching n>1000, k value too big for Proth & NewPGen, using PFGW)
HUNT (832889) (+ side is divisible by 5, - side is divisible by 7)
HURT (833033)
HUTT (833105=5*7*13*1831)
SKYWALKER (80634324010131=3^2*239*37486900981)
LUKE (1019390=2*5*101939)
ANAKIN (643786079=1493*431203)
DARTH (22337621=3251*6871)
VADER (52552035=3^2*5*1167823)

Some notable Base-94 numbers:

www.mersenne.org    (23173464146192129623556375950544=2^4*43*61*2551*11981*2888628773*6254281541)
12345ABCabc`~^&*   
(403838401633020116561588357495=5*2521*29221*2597002043*422179750373)
V?~17OPfwq3an       (15217655020295956113030421=78914411*192837465647382911)
1tRaaRt1                  (102991592304415=5*19*43*25212140099)
https://www.google.com/webhp?hl=en    (5657439476159105326705063160658143662130016410521642446186695866793; The only prime URL I've found so far.)
QuiGon-Jinn (1432756288327546284743), middle of sexy prime triplet (with QuiGon-Jint (1432756288327546284749) and QuiGon-Jinh (1432756288327546284737))

...and many others. :-)