Problems & Puzzles:
Problems
Problem 17. The
largest known sequence of consecutive and reversible
primes.
I found last year (August 3, 1998) the following
sequence:
{1193,1201,1213,1217,1223,1229,1231,1237,1249,1259}
(See the Sloane’s sequence A040104,
and see also my Puzzle
No. 20 )
All of the ten (10) members of this sequence are
consecutive primes and also reversible
(nonpalindromic) primes; this last means that
1193 and 3911 are primes, 1201 and 1021 are primes, and
so on.
As far as I know this is the largest known sequence of
this type.
Questions:
a) Can you find a larger sequence of
this type?
b) Can you find a larger sequence
including palprimes, if necessary?
Felice Russo
has obtained (May 21, 1999) another sequence of 10
consecutive reversible non palindromic primes, 8 digits
each:
{91528739, 91528777, 91528807, 91528817, 91528819,
91528823
91528837, 91528841, 91528903, 91528939}
***
Jud McCranie sent (May 22, 1999) one
more 10 members sequence of consecutive reversible and
non palindromic primes, 9 digits each, starting in
302706311 and ending in 302706493.
***
My feeling (CR) now  after this other two10 members
sequences  is that an eleven members sequence of this
type must exists...
***
Jud
McCranie has gotten  at last, 27/05/99  a sequence of 11 terms: 1477271183 through 1477271387.
Previously he got another sequences of 10 terms:
777528457617
7782869177109
924408493619
and 1177842077 through 1177842269
***
One day after (28/05/99) he
got another larger sequence (12 terms):
form 9387802769 to 9387803033.
Other results from him are:
Terms  From  To:
10  1801280717  1801280867
10  1811906567  1811906743
10  7060718569  7060718747
10  9338212141  9338212381
11  9427522387 
9427522387
***
Giovanni Resta wrote, on March 2011:
I extended the search range of Problem 17
(consecutive emirps) to 10^14 (plus a little bit)
and so I found 5 runs of length 13.
There is a large gap between the first run of length 12 (which starts at
9387802769) and the first run of length 13.
The primes (and their reverses) for the first sequence of length 13,
which starts at 15423094826093, are:
1 15423094826093 39062849032451
2 15423094826147 74162849032451
3 15423094826149 94162849032451
4 15423094826197 79162849032451
5 15423094826213 31262849032451
6 15423094826257 75262849032451
7 15423094826267 76262849032451
8 15423094826287 78262849032451
9 15423094826339 93362849032451
10 15423094826341 14362849032451
11 15423094826351 15362849032451
12 15423094826369 96362849032451
13 15423094826389 98362849032451
The other such sequences of 13 terms
that I found are:
16624937940797  16624937941187
78862056635899  78862056636373
99994515721939  99994515722411
100352695899791  100352695900157
***
