Hello,

> Did anybody look for primes of the form p#^2^n+1

> (or n!^2^n+1)? E.g., 1801#^16+1 is prime.

No, But!,

I did look at 2^n*n#-1 and have assembled my

fragments.

They have a good, neat looking form, but the form is

also flawed. For non-prime n, "proper" notation

would be 2^n*P(pi(n))#-1, ruining the repeating digits

effect in the presentation. When n is prime, the

notational collapse doesn't exist, so whatever these

primes should be called, n has to be prime for it to

be a perfect "whatever...".

There can be circumstances where taking the primorial

of n=composite can create several instances of the

same

number in an iterated run. With this form, the

multipler 2^n ensures each is distinct.

Thus, is it flawful, lawful, awful to say

2^16*16#-1 is prime?

Here's what I have found on these,

any one wants to take it farther,

be my guest.

-Dick

After n=16, they are all PRP's.

I never got around to testing them.

2^2*2#-1 is prime!

2^3*3#-1 is prime!

2^7*7#-1 is prime!

2^8*8#-1 is prime!

2^14*14#-1 is prime!

2^16*16#-1 is prime!

2^18*18#-1

2^20*20#-1

2^40*40#-1

2^42*42#-1

2^44*44#-1

2^53*53#-1

2^134*134#-1

2^154*154#-1

2^185*185#-1

2^187*187#-1

2^191*191#-1

2^197*197#-1

2^200*200#-1

2^201*201#-1

2^230*230#-1

2^235*235#-1

2^239*239#-1

2^244*244#-1

2^256*256#-1

2^282*282#-1

2^303*303#-1

2^358*358#-1

2^489*489#-1

2^536*536#-1

2^665*665#-1

2^684*684#-1

2^719*719#-1

2^1098*1098#-1

2^1204*1204#-1

2^1400*1400#-1

2^1516*1516#-1

2^1629*1629#-1

2^1903*1903#-1

2^1997*1997#-1

2^1999*1999#-1

2^2104*2104#-1

2^2477*2477#-1

2^3075*3075#-1

2^3676*3676#-1

2^3785*3785#-1

2^4115*4115#-1

2^5429*5429#-1

2^5808*5808#-1

2^6069*6069#-1

2^6276*6276#-1

2^9095*9095#-1

2^10423*10423#-1

2^10839*10839#-1

2^16181*16181#-1

2^17521*17521#-1

2^17734*17734#-1

2^20451*20451#-1

2^22560*22560#-1

2^29545*29545#-1

2^30069*30069#-1

2^33389*33389#-1

** Run Stopped at 34952

Here's the largest cofactor PRP's in the run

(2^12804*12804#-1)/15959

(2^15233*15233#-1)/263089

(2^18932*18932#-1)/116981

(2^27766*27766#-1)/1993067

And here are the caps of a couple Sophie Germains,

(no more of these at least to n=918).

2^(53-1)*53#-1 (digits:36 checksum:_8F526EDE_)

2^(201-1)*201#-1 (digits:143 checksum:_E1E2C9AF_)

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