Find some primes that safely contain a pair of emirps. The emirps must be isolated from each other and from the outside world by a digit. It is as if the emirps are matter and anti-matter: they cannot touch or there will be a risk of catastrophic anihilation. And since we cannot tell which one is anti-matter, both must be isolated from each other and also the rest of the world. This is all in accordance with the ancient lore.
(1) What is the smallest 9-digit prime of the form: axyzbzyxc, where xyz and zyx are each 3-digit primes with distinct digits; and each letter a,b,c,x,y,z designates a different digit.
(2) Also find the largest.
(3) Now, same question for an 11-digit prime of the form awxyzbzyxwc; again different letters are distinct digits, where wxyz and zyxw are a pair of 4-digit emirps.
(4) Also find the largest.
Note: Emirps are primes whose reversal is a different prime.
p=primes(999);
clc
emirps=double.empty(0,2);
v=[];
for i=1:length(p)
if p(i)>99
ps=char(string(p(i)));
pr=str2double(flip(ps));
if isprime(pr)
emirps(end+1,:)=[p(i) pr];
end
end
end
for i=1:length(emirps)
for a=1:9
for b=0:9
for c=1:9
s=[char(string(a)) ...
char(string(emirps(i,1))) ...
char(string(b)) ...
char(string(emirps(i,2))) ....
char(string(c))];
if length(unique(s))==6
if isprime(str2double(s))
% disp(s)
v(end+1)=str2double(s);
end
end
end
end
end
end
disp(' ')
sort(v')
p=primes(9999);
emirps=double.empty(0,2);
v=[];
for i=1:length(p)
if p(i)>999
ps=char(string(p(i)));
pr=str2double(flip(ps));
if isprime(pr)
emirps(end+1,:)=[p(i) pr];
end
end
end
for i=1:length(emirps)
for a=1:9
for b=0:9
for c=1:9
s=[char(string(a)) ...
char(string(emirps(i,1))) ...
char(string(b)) ...
char(string(emirps(i,2))) ....
char(string(c))];
if length(unique(s))==7
if isprime(str2double(s))
% disp(s)
v(end+1)=str2double(s);
end
end
end
end
end
end
disp(' ')
sort(v')
finds
(1) 134787439
(2) 975181573
(3) 13067276039
(4) 97643834671
from the full lists below
ans =
134787439
138959837
170989073
174363479
176929673
195343597
198323897
214959413
214989413
215747513
216757613
217949713
217959713
238909831
238909837
238949831
238969837
238979831
270141073
270181073
270949073
270969071
273989371
274383479
275101579
276141673
276181679
276909671
290717093
290767091
293707391
293767391
293787391
295343591
296737691
296757691
298303891
298343891
310767019
314989417
315707519
370949071
370989071
376929671
390727091
390787091
416797613
417959713
438919837
470181079
470929073
475121573
475121579
476131679
476151679
476191673
476989673
495313597
496707691
510727013
514939417
514969417
516787619
534707431
534787439
538909831
570939071
570949073
570989071
573989371
576181673
576989671
590717093
593727391
598303897
610747019
610797013
614939417
614959417
615737519
615787519
617909713
617949713
635929531
635989531
638909837
638929831
638959831
670131079
670929071
673949371
674303479
674393471
694101497
694171493
695323591
714969413
794101493
810727013
810747019
814929413
814969417
814979413
815737519
817959713
834707431
835969531
870121079
870959071
874353479
875141573
876121679
876909673
890767093
894101497
895303597
896727691
897151793
974363471
975181573
ans =
13067276039
13067476039
13089598037
13257075239
13467276439
13467576439
13527672539
17043634079
17043834079
17459295473
17523632579
17529092573
17589698573
17603230679
17643834679
17649594673
17649894673
19257875293
19467576493
19857075893
21409390417
21409690417
21453635419
21583938517
21597679513
21657475613
21789698713
23049594031
23049894031
23089198037
23109690137
23469596431
23541614539
23571417539
23697079631
27459095471
27459895471
27561416579
27589098571
27589198573
27649594673
27649894673
27681918673
27963036971
29013531097
29041514093
29467076491
29547674591
29601410693
29613831697
29643534691
29643834697
29803630891
29857075891
29857175893
29857475891
29857675891
29871017893
31249594217
31249894217
31409890417
37649094671
37649894671
39241514297
39521812597
41237873219
41259895213
41283038219
41283538217
41523632519
41523832517
41723832719
41867576819
43089298037
43169096137
43257675239
43527072539
43571217539
43571817539
43821612839
47253635279
47529892573
47589098573
47589298573
47603830679
47681518673
47901610973
49257675293
49521812597
49601310697
49781518793
49803530891
49803530897
51069296017
51069396017
51069796013
51237473219
51237673219
51409690417
51429092417
51789498713
51867376819
51867976813
53019891037
53049294031
53049294037
53067876031
53089498037
53089798031
53109290137
53169896137
53271417239
53271617239
53407270439
53467876439
53467976431
53469296431
57321012379
57901810973
57963236971
59041714093
59241014297
59241614293
59403630491
59421612493
59437073491
59467176493
59467376491
59601310697
59643034697
59643834697
59871017893
61237573219
61249894213
61259095217
61283438219
61283938217
61429892413
61487078413
61523432519
61583738519
61723832719
61789598713
61847374819
63019891037
63089298037
63109290137
63251015237
63407170439
63821712839
63851415839
67043534071
67253035271
67349294371
67529892571
67589098573
67589298571
67589398571
67841014873
67841914873
69013231097
69103830197
69127872193
69241514297
69257475293
69521812597
69803530891
69871217893
71283038219
71283638219
71409690413
71523832519
73251815239
79241514293
79421512493
79601210693
79803230891
81249694213
81259695217
81279097213
81409590413
81429092417
81429692413
81429692417
81523632517
81657375619
81753435719
83049294037
83049594031
83049694031
83067976031
83169296137
83271017239
83271417239
83407170439
83407570439
83467176439
83469096437
83541014537
83541914537
83571017539
87219091273
87253435271
87321612379
87459295471
87529392571
87529492571
87529492573
87529692571
87603130679
87643034671
87649294673
87963536971
89257675291
89403230491
89421012497
89467176493
89521612597
89547174593
89643234691
91283538217
91487078413
91487678413
91583038517
93067276031
93541214537
93821012837
97523032571
97523632571
97643834671
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Posted by Charlie
on 2023-10-19 10:02:26 |
computer solution
