[ October 18, 2004 ]
Two Prime Numbers starting from 18 and 19
Farideh Firoozbakth (email)

Farideh Firoozbakht from Iran
found two nice probable primes  p1 and p2
formed by concatenating the integers
from 18 resp. 19 up to 3607 resp. 1471.

181920... ...36063607 (13296 digits)
and
192021... ...14701471 (4750 digits)

hitherto unknown in the prime number community.
Note that the endnumbers 1471 and 3607 of the strings
are primes, as well as 'their' concatenation 14713607 !

Farideh found these primes by using Mathematica that she
masters during 15 years now. "It is as necessary to me as air"
she writes in one of her messages.

Mathematica says p1 & p2 are primes, i.e.,

In[21]:= {PrimeQ[p1],PrimeQ[p2]}

Out[21]= {True, True}

Note that the built-in primality testing function PrimeQ
does not actually give a proof that a number is prime.
However, there are no known examples where PrimeQ fails.

In Mathematica we can generate p1 & p2 in this way :

p1=(v1={};Do[v1=Join[v1,IntegerDigits[k]],{k,18,3607}];FromDigits[v1])

p2=(v1={};Do[v1=Join[v1,IntegerDigits[k]],{k,19,1471}];FromDigits[v1])

And Mathematica determines length of p1 & p2 in this way:

In[24]:= Length[IntegerDigits[p1]]
Out[24]= 13296

In[25]:= Length[IntegerDigits[p2]]
Out[25]= 4750

With the aid of the freeware tool PFGW ( PrimeForm)
I (PDG) could verify Farideh's results.
PFGW has a built-in function for Smarandache sequences 'Sm'.
Using the double coordinates Sm(x,y) makes for a circular
shift starting from y, so I had to divide the string with
the length of the shifted part. PFGW always rounds up
till an integer is left over. Reals cannot be input evidently.
Here are the commands and timings on my system
(Pentium 4 at 3 GHz) :

The lengths of the numbers can be determined as follows :

The Reference Table for
Smarandache Concatenated Numbers
with starting numbers from 1 to 19.
Maybe you like to participate ?

Further reading and exploring
Entries of F. Firoozbakht in Prime Curios!
Primes by Listing
Consecutive Number Sequences