WON plate148 | World!OfNumbers [ May 4, 2003 ] Concatenate two neighbouring primes (none, one or maximum two primes skipped)so that you end up with a square A simple search puzzle... with hard to find solutions

GIVE ME TWO PRIMES FOR A SQUARE PLEASE
SKIP PRIMESCONCATENATED
PRIMESET
ROOTAUTHOR
0
two successive
primes
1411828016678198512725064549221
411828016678198512725064549241
641738277398347583345401533579
= p
= q
=
¯¯¯pq
Giovanni
Resta
2pq
¯¯¯pq
?
3pq
¯¯¯pq
?
4pq
¯¯¯pq
?
5pq
¯¯¯pq
?
RNDpq
¯¯¯pq
?

1
one prime
skipped
1255pdg
2623387623401789549pdg
3p > 100,000,000q
¯¯¯pq
pdg
4pq
¯¯¯pq
?
5pq
¯¯¯pq
?
RNDpq
¯¯¯pq
?

2
two primes
skipped
1476169pdg
2p > 100,000,000q
¯¯¯pq
pdg
3pq
¯¯¯pq
?
4pq
¯¯¯pq
?
5pq
¯¯¯pq
?
RNDpq
¯¯¯pq
?

[ May 7, 2003 ]
Jean Claude Rosa considered the case p > q
and found the following nice solutions :

1one primeskipped 1 jcr 2137 2129 4623 809821 809801 899901 p q √¯¯¯pq p q √¯¯¯pq

[ May 17, 2003 ]
Giovanni Resta (email) found the smallest solution
for the case with no gaps : p(k)p(k+1) = x2

411828016678198512725064549221 || 411828016678198512725064549241 =
6417382773983475833454015335792

For the reverse case whereby p > q or p(k)p(k-1) = x2
he found the following three solutions :

607286296388662783 || 607286296388662769 =
7792857604169748872

999800009999800021 || 999800009999800001 =
9998999999999000012

126896403745276627317710453 || 126896403745276627317710401 =
3562252149206687296285539512

A000148 Prime Curios! Prime Puzzle
Wikipedia 148 Le nombre 148
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