--- In

primenumbers@yahoogroups.com, "Paul Underwood"

<paulunderwood@...> wrote:

>

> Enter 2^y-y into http://www.primenumbers.net/prptop/searchform.php

to

> see gigantic PrPs:

>

> 9 2^505431-505431 152150 Henri Lifchitz 04/2005

> 10 2^500899-500899 150786 Henri Lifchitz 04/2005

> 11 2^481801-481801 145037 Henri Lifchitz 03/2005

> 108 2^228271-228271 68717 Henri Lifchitz 11/2004

> 170 2^182451-182451 54924 Henri Lifchitz 10/2004

> 509 2^108049-108049 32526 Henri Lifchitz 11/2001

> 2527 2^61011-61011 18367 Henri Lifchitz 09/2001

> 2534 2^60975-60975 18356 Henri Lifchitz 09/2001

> 5891 2^44169-44169 13297 Henri Lifchitz 09/2001

>

> There may be more sub-giantic ones,

Using PFGW, I have found all those with < 10000 digits:-

2^2-2 prime by PFGW

2^3-3 prime by PFGW

2^9-9 prime by PFGW

2^13-13 prime by PFGW

2^19-19 prime by PFGW

2^21-21 prime by PFGW

2^55-55 prime by PRIMO 0s

2^261-261 prime by PRIMO 0.06s

2^3415-3415 prime by PRIMO 47mn 6s

2^4185-4185 prime by PRIMO 2h 3mn 22s

2^7353-7353 prime by PRIMO 23h 20mn 22s

2^12213-12213 137-PRP by PFGW [PRIMO certification would take c. 6

days]

[

BTW when Werner said:

>Thanks to all! MuPAD confirms:

>2^n-n is prime for n=3415, 4185, 7353.

I think he was being optimistic, and should have said "probable

prime", no?

]

I've done the same for 2^n+n.

Henri's site

http://www.primenumbers.net/prptop/searchform.php
gives:

3 2^678561+678561 204268 Henri Lifchitz 05/2006

137 2^204129+204129 61449 Henri Lifchitz 04/2002

937 2^88071+88071 26513 Henri Lifchitz 09/2001

so the first of these is the 3rd-largest PRP known.

And to complete the picture, here are all those with < 10000 digits :-

2^1+1 prime by PFGW

2^3+3 prime by PFGW

2^5+5 prime by PFGW

2^9+9 prime by PFGW

2^15+15 prime by PFGW

2^39+39 prime by VFYPR 0 sec

2^75+75 prime by VFYPR 0 sec

2^81+81 prime by VFYPR 0 sec

2^89+89 prime by VFYPR 0 sec

2^317+317 prime by VFYPR 2 sec

2^701+701 prime by VFYPR 60 sec

2^735+735 prime by VFYPR 71 sec

2^1311+1311 prime by VFYPR 1484 sec

2^1881+1881 prime by VFYPR 11991 sec

2^3201+3201 prime by PRIMO 48mn 23s

2^3225+3225 prime by PRIMO 38mn 50s

2^11795+11795 137-PRP by PFGW (PRIMO certification would take c. 5

days)

All timings are for a 1.2 GHz PC.

Anyone want to do those 2 bigger certifications with PRIMO?

-Mike Oakes