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

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 https://groups.yahoo.com/neo/groups/primeform/conversations/topics/4042
David Broadhurst informed me that in the past http://groups.yahoo.com/group/primeform/files/HD/patrick.zip you could have found 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 ) could once 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 was 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 was once 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 once 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 Number Theory List - Message 5 aug 2003 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) Prime Curios 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 ] Prime Curios 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 ] Prime Curios 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 ] Prime Curios 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)