World!Of
Numbers
WON plate
|

[ 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 :

1
one prime skipped		 12137 2129 4623jcr
2809821809801899901jcr
3pq
√¯¯¯pq
?
RNDpq
√¯¯¯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

[ TOP OF PAGE]

( © All rights reserved )
Patrick De Geest - Belgium - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com