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WON plate
150 |


Top3000+ palindromic primes with prime digits.
Update from [ March 4, 2006 ]

This WONplate will be the home port for the Top3000+
palindromic primes consisting solely of prime digits
[ 2, 3, 5 & 7 ] above 3000 digits.

I haven't made a careful search of the internet as yet to find all
possible candidates. So if any reader can find a palprime
not included in the table, please feel free to submit it.

Nr. 1
36401
decimal digits
Let R(n) = (10^n–1)/9 be the n-digit base-10 repunit and
c = 42000040044444004000024
Then N = 34*R(36400)c*10^2264*R(36400)/R(4550) – 1
or N = 37777777777777777... ...77777777777777773

The long flow of 7's in the decimal expansion is eight times
'interrupted' with the string 35777737733333773777753.
by David Broadhurst (email) [December 12, 2003 ]
37777...77773 (36401-digits)
Its formula and proof are described in PrimeForm
http://groups.yahoo.com/group/primeform/message/4042

David Broadhurst informed me that in
http://groups.yahoo.com/group/primeform/files/HD/patrick.zip
you will find the kernels of the proofs for palprimes
with 30913, 24421, 20911, 17941, 15601, 7201 and 4201 prime digits.

Nr. 2
30913
decimal digits
Let R(n) = (10^n–1)/9 be the n-digit base-10 repunit and
c = 400440004440040044000000000440040044400044004
Then N = 34*R(30912)c*10^1266*R(30912)/R(2576) – 1
or N = 37777777777777777... ...77777777777777773

The interesting bits are inside ! To see them do
pfgw –l –od –q"34*R(30912)–c*10^1266*R(30912)/R(2576)–1"
and look in pfgw.out
by David Broadhurst (email) [August 5, 2003 ]
From the Number Theory List :
30913-digit palindromic prime with prime digits
D. Broadhurst list of palprimes with prime digits
The result of the BLS test ( hd30913.out ) using the prime factors
in the helper file ( hd30913.fac ) can be extracted from
http://groups.yahoo.com/group/primeform/files/HD/patrick.zip
including the KP calling routines as for 15601 digits, and above,
KP proofs are needed.
Extract complete proof for this 30913-digit record holder from
http://physics.open.ac.uk/~dbroadhu/cert/kp30913.zip
Nrs. 3-4
24421
decimal digits
3373773737737333337377373773734*R(24420)/R(30) – 1
3335335333333553553333335335332*R(24420)/R(30) + 1
by David Broadhurst (email) [2003 ]
D. Broadhurst list of palprimes with prime digits
For 15601 digits, and above, KP proofs are needed.
Nrs. 5-9
20911
decimal digits
3737737773337373737333777377374*R(20910)/R(30) – 1
3533335335353355533535335333352*R(20910)/R(30) + 1
3353333555353335333535553333532*R(20910)/R(30) + 1
3335555355335535355335535555332*R(20910)/R(30) + 1
3333777733773337333773377773334*R(20910)/R(30) – 1
by David Broadhurst (email) [October, 2003 ]
D. Broadhurst list of palprimes with prime digits
For 15601 digits, and above, KP proofs are needed.
Nrs. 10-18
17941
decimal digits
3737333737777737377777373337374*R(17940)/R(30) – 1
3555333353535533355353533335552*R(17940)/R(30) + 1
3355553335353335333535333555532*R(17940)/R(30) + 1
3353553553535533355353553553532*R(17940)/R(30) + 1
3335533355553553553555533355332*R(17940)/R(30) + 1
3333777333333733373333337773334*R(17940)/R(30) – 1
3333733373737777777373733373334*R(17940)/R(30) – 1
3333533355335533355335533353332*R(17940)/R(30) + 1
3333377373333733373333737733334*R(17940)/R(30) – 1
by David Broadhurst (email) [August, 2003 ]
D. Broadhurst list of palprimes with prime digits
For 15601 digits, and above, KP proofs are needed.
Nr. 19
15769
decimal digits
3(7)157673 = 377777... ...777773
(34*10^15768-43)/9 = 7*(10^15769-1)/9-4*(10^15768+1)

by Greg Childers (email) [February 28, 2006 ]
The complete proof of (34*10^15768-43)/9 with both
the Primo and CHG certificates is posted at
http://www.pa.uky.edu/~childers/certs/P15769.zip
This is a fine proof, combining state-of-the-art factorization
with three types of primality testing and proving
(BLS, CHG, ECPP). David Broadhurst added this prime also in
the "Caldwell-illegitimate" appendix located at
http://groups.yahoo.com/group/primeform/files/NTG/gigantic.txt

Plateau and Depression Primes (PDP's)
Nrs. 20-26
15601
decimal digits
3777733777333777773337773377774*R(15600)/R(30) – 1
3773373773733373733373773733774*R(15600)/R(30) – 1
3553555553353335333533555553552*R(15600)/R(30) + 1
3535335533353553553533355335352*R(15600)/R(30) + 1
3333733337337373737337333373334*R(15600)/R(30) – 1
3333553333335353535333333553332*R(15600)/R(30) + 1
3333353535553333333555353533332*R(15600)/R(30) + 1
by David Broadhurst (email) [July 3, 2003 ]
http://groups.yahoo.com/group/primeform/message/3404
D. Broadhurst list of palprimes with prime digits
For 15601 digits, and above, KP proofs are needed.
Nr. 27
12271
decimal digits
3777333333777337337773333337774*R(12270)/R(30) – 1
by Ralph Twain [2003 ]
D. Broadhurst list of palprimes with prime digits
Nr. 28
8205
decimal digits
37773733733337373333733737774*R(8204)/R(28) – 1
by Ralph Twain [2003 ]
D. Broadhurst list of palprimes with prime digits
Nr. 28-128
7201
decimal digits
A hundred-pack !!
3777777333377737737377377733337777774 *
R(7200)/R(36) – 1

...
downto
...
3333333377733737773777373377733333334 *
R(7200)/R(36) – 1

by David Broadhurst (email) [September, 2003 ]
Complete list D. Broadhurst list of palprimes with prime digits
Nr. 129
7141
decimal digits
(30*R(17)+2)*R(7140)/R(17) + 1
by David Broadhurst (email) [2003 ]
D. Broadhurst list of palprimes with prime digits
Nr. 130
6959
decimal digits
3(23)3479 = (32*10^6959-23)/99
by Hans Rosenthal (email) [July 7, 2003 ]
Primo Top-20 (gold)
32323...32323 (6959-digits)
Smoothly Undulating Palindromic Primes (SUPP's)
Nr. 131
6249
decimal digits
7(57)3124 = (75*10^6249-57)/99
by Hans Rosenthal (email) [August 21, 2003 ]
Primo Top-20 (silver)
Smoothly Undulating Palindromic Primes (SUPP's)
Nr. 132
4909
decimal digits
Let R(n) = (10^n–1)/9 be the n-digit base-10 repunit and
c = 4000044040404400004
Then N = 34*R(4908)c*10^400*R(4908)/R(818) – 1

by Ralph Twain [2003 ]
D. Broadhurst list of palprimes with prime digits
Nr. 133
4261
decimal digits
(30*R(15)+4)*R(4260)/R(15) – 1 or
33333333(333333373333333)28333333333

by Phil Carmody and David Broadhurst [June 27, 2003 ]
http://groups.yahoo.com/group/primeform/message/3390
D. Broadhurst list of palprimes with prime digits
Nr. 134-1528
4201
decimal digits
A 1395-pack !!
3777777777377733773333333773377737777777774 *
R(4200)/R(42) – 1

...
downto
...
3333333333333533533553553353353333333333332 *
R(4200)/R(42) + 1

by David Broadhurst (email) [September, 2003 ]
Complete list D. Broadhurst list of palprimes with prime digits
Nr. 1529
4159
decimal digits
(30*R(14)+2)*R(4158)/R(14) + 1
by David Broadhurst [2003 ]
D. Broadhurst list of palprimes with prime digits
Nr. 1530
4157
decimal digits
3(53)2078 = (35*10^4157-53)/99
by Hans Rosenthal (email) [Feb 11, 2002 ]
35353...35353 (4157-digits)
Smoothly Undulating Palindromic Primes (SUPP's)
Nr. 1531
3407
decimal digits
3(23)1703 = (32*10^3407-23)/99
by Hans Rosenthal (email) [Oct 19, 2001 ]
32323...32323 (3407-digits)
Smoothly Undulating Palindromic Primes (SUPP's)
Nr. 1532
3381
decimal digits
3(7)33793 =
(34*10^3380-43)/9 = 7*(10^3381-1)/9-4*(10^3379+1)

by Patrick De Geest (email) [September 19, 2003 ]
Plateau and Depression Primes (PDP's)
Nr. 1533
3147
decimal digits
3(53)1573 = (35*10^3147-53)/99
by Hans Rosenthal (email) [Oct 19, 2001 ]
Smoothly Undulating Palindromic Primes (SUPP's)
Nr. 1534
3037
decimal digits
3(2)30353 =
(29*10^3036+7)/9 = 2*(10^3037-1)/9+(10^3036+1)

by Patrick De Geest (email) [August 2, 2003 ]
32222...22223 (3037-digits)
Plateau and Depression Primes (PDP's)
Nr. 1535
3015
decimal digits
3(23)1507 = (32*10^3015-23)/99
by Hans Rosenthal (email) [Oct 19, 2001 ]
Smoothly Undulating Palindromic Primes (SUPP's)


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