- Hi All,

The following descibe AP13s with 83 digits

(9773795412+$n*81373857)*181#+1 n=0-12

(7967748420+$n*340308346)*181#+1) n=0-12

Input/output statistics:-

Numbers input to NewPGen: 3*10^9 seived to 1*10^11

Nubers input to PFGW 626824792. PRP's found by PFGW: 148388269

AP13 search run against the PRPs in the first 4*10^6 of the numbers (exhaustively finding all AP in the 3*10^9 range)

I know some, Mike at least, appreciate stats so

AP07s:14260855

AP08s:601980

AP09s:26092

AP10s:1215

AP11s:58

AP12s:2

AP13s:0

Additional APs through extension of ap7'3 through 12's (both forward and back)gave additional

AP08s:773320

AP09s:69921

AP10s:4908

AP11s:288

AP12s:12

AP13s:2

First Ap13

Primality testing (9773795412+0*81373857)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 191

Calling Brillhart-Lehmer-Selfridge with factored part 35.77%

(9773795412+0*81373857)*181#+1 is prime! (0.0047s+0.0016s)

Primality testing (9773795412+1*81373857)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 2

Calling Brillhart-Lehmer-Selfridge with factored part 33.58%

(9773795412+1*81373857)*181#+1 is prime! (0.0042s+0.0017s)

Primality testing (9773795412+2*81373857)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 197

Running N-1 test using base 199

Calling Brillhart-Lehmer-Selfridge with factored part 33.94%

(9773795412+2*81373857)*181#+1 is prime! (0.0061s+0.0017s)

Primality testing (9773795412+3*81373857)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 3

Calling Brillhart-Lehmer-Selfridge with factored part 34.67%

(9773795412+3*81373857)*181#+1 is prime! (0.0043s+0.0017s)

Primality testing (9773795412+4*81373857)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 211

Running N-1 test using base 227

Calling Brillhart-Lehmer-Selfridge with factored part 33.58%

(9773795412+4*81373857)*181#+1 is prime! (0.0062s+0.0018s)

Primality testing (9773795412+5*81373857)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 7

Calling Brillhart-Lehmer-Selfridge with factored part 34.31%

(9773795412+5*81373857)*181#+1 is prime! (0.0047s+0.0019s)

Primality testing (9773795412+6*81373857)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 223

Calling Brillhart-Lehmer-Selfridge with factored part 33.58%

(9773795412+6*81373857)*181#+1 is prime! (0.0047s+0.0017s)

Primality testing (9773795412+7*81373857)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 11

Calling Brillhart-Lehmer-Selfridge with factored part 35.40%

(9773795412+7*81373857)*181#+1 is prime! (0.0046s+0.0017s)

Primality testing (9773795412+8*81373857)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 193

Running N-1 test using base 239

Calling Brillhart-Lehmer-Selfridge with factored part 35.40%

(9773795412+8*81373857)*181#+1 is prime! (0.0059s+0.0019s)

Primality testing (9773795412+9*81373857)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 19

Calling Brillhart-Lehmer-Selfridge with factored part 35.77%

(9773795412+9*81373857)*181#+1 is prime! (0.0044s+0.0017s)

Primality testing (9773795412+10*81373857)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 229

Calling Brillhart-Lehmer-Selfridge with factored part 35.04%

(9773795412+10*81373857)*181#+1 is prime! (0.0047s+0.0017s)

Primality testing (9773795412+11*81373857)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 23

Calling Brillhart-Lehmer-Selfridge with factored part 35.40%

(9773795412+11*81373857)*181#+1 is prime! (0.0044s+0.0017s)

Primality testing (9773795412+12*81373857)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 241

Calling Brillhart-Lehmer-Selfridge with factored part 34.67%

(9773795412+12*81373857)*181#+1 is prime! (0.0043s+0.0017s)

2nd Ap13

Primality testing (7967748420+0*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 191

Calling Brillhart-Lehmer-Selfridge with factored part 34.67%

(7967748420+0*340308346)*181#+1 is prime! (0.0044s+0.0016s)

Primality testing (7967748420+1*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 199

Calling Brillhart-Lehmer-Selfridge with factored part 35.40%

(7967748420+1*340308346)*181#+1 is prime! (0.0049s+0.0018s)

Primality testing (7967748420+2*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 197

Calling Brillhart-Lehmer-Selfridge with factored part 35.04%

(7967748420+2*340308346)*181#+1 is prime! (0.0048s+0.0015s)

Primality testing (7967748420+3*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 193

Calling Brillhart-Lehmer-Selfridge with factored part 34.31%

(7967748420+3*340308346)*181#+1 is prime! (0.0040s+0.0017s)

Primality testing (7967748420+4*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 229

Calling Brillhart-Lehmer-Selfridge with factored part 35.40%

(7967748420+4*340308346)*181#+1 is prime! (0.0046s+0.0018s)

Primality testing (7967748420+5*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 223

Calling Brillhart-Lehmer-Selfridge with factored part 35.40%

(7967748420+5*340308346)*181#+1 is prime! (0.0045s+0.0015s)

Primality testing (7967748420+6*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 233

Calling Brillhart-Lehmer-Selfridge with factored part 33.58%

(7967748420+6*340308346)*181#+1 is prime! (0.0045s+0.0014s)

Primality testing (7967748420+7*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 227

Calling Brillhart-Lehmer-Selfridge with factored part 34.31%

(7967748420+7*340308346)*181#+1 is prime! (0.0046s+0.0018s)

Primality testing (7967748420+8*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 239

Running N-1 test using base 241

Calling Brillhart-Lehmer-Selfridge with factored part 35.04%

(7967748420+8*340308346)*181#+1 is prime! (0.0058s+0.0015s)

Primality testing (7967748420+9*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 211

Calling Brillhart-Lehmer-Selfridge with factored part 33.94%

(7967748420+9*340308346)*181#+1 is prime! (0.0044s+0.0014s)

Primality testing (7967748420+10*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 197

Calling Brillhart-Lehmer-Selfridge with factored part 33.45%

(7967748420+10*340308346)*181#+1 is prime! (0.0044s+0.0014s)

Primality testing (7967748420+11*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 251

Calling Brillhart-Lehmer-Selfridge with factored part 33.82%

(7967748420+11*340308346)*181#+1 is prime! (0.0058s+0.0015s)

Primality testing (7967748420+12*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 233

Calling Brillhart-Lehmer-Selfridge with factored part 34.55%

(7967748420+12*340308346)*181#+1 is prime! (0.0047s+0.0015s)

Primality testing (7967748420+13*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

Cheers

Ken - --- In primeform@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
>

OK, seen it.

>

>

> --- In primeform@yahoogroups.com,

> "ajo" <sopadeajo2001@> wrote:

>

> > Is there more (or less?) probability to find long prime p(n)

> > chains with n beginning at n=0 or with n>=n0 for arbitrary n0.

>

> The case n >= n0 >= 0 is subsumed by my case, with n >= 0,

> Suppose that k*b^n + 1 is prime in the L cases n = n0 .. n0+L-1,

> then K*b^n + 1 is prime in the L cases n = 0 .. L-1

> where K = k*b^n0.

>

> Reminder: The challenge is

>

> > find more than 11 primes p[n] with p[n]-1 forming a

> > geometric progression with a ratio b > 265

>

> David

>