Thread for posting tiny primes - Page 65

CRGreathouse · 2010-09-26, 06:11

Quote:

Originally Posted by 3.14159

Precisely. The strawmen were invalid.

The range I used was k = 1 to 5000.

So when you say, "the strawmen were invalid", you mean, "the claim I made was false, the number may have prime factors below 1150 digits".

CRGreathouse · 2010-09-26, 06:16

Quote:

Originally Posted by 3.14159

A prime with only 6s and 7s as digits:

Code:

7677676676677777767677677666676767676766677677677767677677767776776767676667776677667776666676766766777676767666767667776676767776676766776767676766766666666676677776776666777777777777777777777777777777777777777777777777777777 (226 digits)

Ha!

227 digits:

Code:

66666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667677677

cmd · 2010-09-26, 13:14

Quote:

Originally Posted by CRGreathouse

227 digits:

Code:

66666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667677677

( But make the case that units digit position always be 7 )

cmd notation bdpq ... 7 = p

3.14159 · 2010-09-26, 13:59

Quote:

Originally Posted by cmd

( But make the case that units digit position always be 7 )

cmd notation bdpq ... 7 = p

Go hijack another thread, please..

3.14159 · 2010-09-26, 14:00

Submissions: (23411757051*887!+1)/86336291 (2234 digits)

The best I could manage is to get this number as a PRP.

(561865705694449011987288232617124899208796671193597755*1597!+1)/(9688*24!^2+1) (4427 digits)

316 * 450!^2 + 1 (2003 digits)

Verification:
Primality testing 316*450!^2+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 461
Generic modular reduction using generic reduction FFT length 640 on A 6654-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 38.00%
316*450!^2+1 is prime! (0.2430s+0.0518s)

kar_bon · 2010-09-26, 15:03

Entry for No.6:

PFGW Version 3.3.6.20100908.Win_Stable [GWNUM 25.14]
Primality testing 1850*9973#+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Calling Brillhart-Lehmer-Selfridge with factored part 33.34%
1850*9973#+1 is prime!

4302 digits.

3.14159 · 2010-09-26, 15:56

Entry accepted. The current record for k * p(n)# + 1, I think, stands at 4302 digits, by Karsten.

science_man_88 · 2010-09-26, 16:16

it's my birthday I would show the birthday rhyme of happy birthday i made but it's not going to get any laughs.

3.14159 · 2010-09-26, 16:45

Happy birthday, whoever you may be.

kar_bon · 2010-09-26, 18:00

PFGW Version 3.3.6.20100908.Win_Stable [GWNUM 25.14]
Primality testing 892*19997#+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 20021
Calling Brillhart-Lehmer-Selfridge with factored part 33.34%
892*19997#+1 is prime! (27.0340s+0.0023s)

8605 digits

kar_bon · 2010-09-26, 19:41

PFGW Version 3.3.6.20100908.Win_Stable [GWNUM 25.14]
Primality testing 535*30011#+1 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 7
Running N-1 test using base 11
Running N+1 test using discriminant 19, base 1+sqrt(19)
Calling N-1 BLS with factored part 100.00% and helper 0.01% (300.01% proof)
535*30011#+1 is prime! (222.7473s+0.0044s)

12928 digits

2010-09-26, 14:00	#709
3.14159 May 2010 Prime hunting commission. 2⁴·3·5·7 Posts	Submissions: (23411757051887!+1)/86336291 (2234 digits) The best I could manage is to get this number as a PRP. (5618657056944490119872882326171248992087966711935977551597!+1)/(968824!^2+1) (4427 digits) 316 450!^2 + 1 (2003 digits) Verification: Primality testing 316450!^2+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 461 Generic modular reduction using generic reduction FFT length 640 on A 6654-bit number Calling Brillhart-Lehmer-Selfridge with factored part 38.00% 316450!^2+1 is prime! (0.2430s+0.0518s) Last fiddled with by 3.14159 on 2010-09-26 at 14:14

2010-09-26, 15:03	#710
kar_bon Mar 2006 Germany 101101011100₂ Posts	Entry for No.6: PFGW Version 3.3.6.20100908.Win_Stable [GWNUM 25.14] Primality testing 18509973#+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Calling Brillhart-Lehmer-Selfridge with factored part 33.34% 18509973#+1 is prime!** 4302 digits. Last fiddled with by kar_bon on 2010-09-26 at 15:03

2010-09-26, 15:56	#711
3.14159 May 2010 Prime hunting commission. 2⁴×3×5×7 Posts	Entry accepted. The current record for k * p(n)# + 1, I think, stands at 4302 digits, by Karsten. Last fiddled with by 3.14159 on 2010-09-26 at 15:58

2010-09-26, 16:16	#712
science_man_88 "Forget I exist" Jul 2009 Dumbassville 20C0₁₆ Posts	off topic it's my birthday I would show the birthday rhyme of happy birthday i made but it's not going to get any laughs.

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2010-09-26, 16:45	#713
3.14159 May 2010 Prime hunting commission. 2⁴×3×5×7 Posts	Happy birthday, whoever you may be.

2010-09-26, 18:00	#714
kar_bon Mar 2006 Germany 2²×727 Posts	PFGW Version 3.3.6.20100908.Win_Stable [GWNUM 25.14] Primality testing 89219997#+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 20021 Calling Brillhart-Lehmer-Selfridge with factored part 33.34% 89219997#+1 is prime! (27.0340s+0.0023s) 8605 digits

2010-09-26, 19:41	#715
kar_bon Mar 2006 Germany 2²·727 Posts	PFGW Version 3.3.6.20100908.Win_Stable [GWNUM 25.14] Primality testing 53530011#+1 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 7 Running N-1 test using base 11 Running N+1 test using discriminant 19, base 1+sqrt(19) Calling N-1 BLS with factored part 100.00% and helper 0.01% (300.01% proof) 53530011#+1 is prime! (222.7473s+0.0044s) 12928 digits