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unprimeable numbers
A composite number  $n$  is called unprimeable if it cannot be turned into a prime by changing a single digit.

For example, 144 is not unprimeable, because changing the last digit into a nine we obtain 149, a prime. The number 200 is instead unprimeable (the smallest one), since none of the numbers 201, 203, 207, 205, and 209 are prime and all the other numbers which can be obtained from 200 (say, 300, or 270, or 208) are even, so they are not prime.

It is easy to prove that unprimeable numbers are infinite, since, for example, all the numbers of the form  $510+k\cdot 2310$  are unprimeable.

A prime which cannot be turned into another prime by changing a single digit is called weakly prime.

Up to  $10^7$  there are 2855169 unprimeable numbers.

The smallest unprimeable numbers ending in 1, 3, 7 and 9 are, 595631, 1203623, 872897, and 212159, respectively.

The first unprimeable numbers are 200, 204, 206, 208, 320, 322, 324, 325, 326, 328, 510, 512, 514, 515, 516, 518, 530, 532, 534 more terms

Unprimeable numbers can also be... (you may click on names or numbers and on + to get more values)

ABA 200 324 512 + 9981512 aban 200 204 206 + 10000000 abundant 200 204 208 + 10000000 Achilles 200 1352 6728 + 9984600 admirable 532 534 894 + 9999892 alternating 325 890 892 + 9898985 amenable 200 204 208 + 10000000 amicable 6232 10744 66992 + 9892936 apocalyptic 620 624 840 + 30000 arithmetic 204 206 322 + 9999986 astonishing 204 21252 automorphic 625 90625 890625 Bell 4140 betrothed 1648 1925 9504 + 9247095 binomial 325 1140 1330 + 9997156 brilliant 1293671 4134953 4749187 + 9298061 c.heptagonal 1072 4166 4922 + 9990436 c.nonagonal 325 2485 4186 + 9997156 c.octagonal 625 27225 30625 + 9579025 c.pentagonal 1266 2326 4306 + 9985006 c.square 3785 5725 9385 + 9959185 c.triangular 514 1135 1684 + 9965260 cake 1794 2048 2325 + 9585732 Carmichael 449065 825265 1050985 + 9582145 Catalan 16796 208012 2674440 compositorial 17280 congruent 206 208 320 + 9999988 constructible 204 320 510 + 8947712 cube 512 10648 21952 + 9800344 Cunningham 325 530 624 + 9991922 Curzon 326 510 530 + 9999954 cyclic 515 535 895 + 9999985 D-number 10815 188235 1527435 + 6340995 d-powerful 518 1074 1672 + 9999752 de Polignac 3505 3665 4195 + 9999775 decagonal 3052 5365 6930 + 9955602 deficient 206 322 325 + 9999988 dig.balanced 204 518 532 + 9999982 double fact. 46080 645120 droll 9984 17280 39424 + 9461760 Duffinian 324 325 512 + 9999965 eban 2040 2042 2044 + 6066056 economical 320 512 625 + 10000000 emirpimes 326 514 538 + 9999965 enlightened 2048 2560 25000 + 5117695 equidigital 320 896 1072 + 9999625 eRAP 4716 5368 13350 + 9952712 esthetic 898 3232 3234 + 9878765 Eulerian 14608 32752 156190 455192 evil 204 320 325 + 10000000 factorial 5040 40320 362880 3628800 fibodiv 3248 4555 5466 + 9749994 Fibonacci 2584 46368 196418 + 9227465 Friedman 625 1260 1792 + 992256 frugal 512 625 1715 + 10000000 gapful 200 1070 1130 + 10000000 Gilda 628 38006 73805 + 3606368 happy 208 320 326 + 10000000 harmonic 18600 18620 32760 + 8872200 Harshad 200 204 320 + 10000000 heptagonal 2512 3744 4558 + 9917172 hexagonal 325 3486 4186 + 9997156 highly composite 840 1260 1680 + 8648640 hoax 516 535 895 + 9999895 house 1716 15962 28882 + 9418784 hyperperfect 325 iban 200 204 320 + 777774 iccanobiF 514 12815 61135 9679838 idoneal 840 impolite 512 2048 32768 + 8388608 inconsummate 326 516 536 + 999995 interprime 324 515 532 + 9999982 Jordan-Polya 512 1920 2048 + 8847360 junction 204 206 208 + 9999955 Kaprekar 7272 38962 466830 + 9372385 katadrome 320 510 530 + 9876542 Lehmer 3145 7735 9265 + 9946615 Leyland 320 512 16580 + 1058576 lonely 1340 1342 1344 + 4652430 Lucas 322 439204 1860498 lucky 535 895 1645 + 9999855 Lynch-Bell 324 624 1764 + 9867312 magic 6924 16400 21455 + 9841635 magnanimous 512 518 536 + 9171170 metadrome 1268 1345 1346 + 2345678 modest 206 515 622 + 9986666 Moran 516 518 846 + 9999950 Motzkin 2188 41835 113634 narcissistic 54748 nialpdrome 200 320 322 + 10000000 nonagonal 204 325 1350 + 9992125 nude 324 515 624 + 9999648 O'Halloran 204 oban 320 325 326 + 898 octagonal 1680 3816 5720 + 9999176 odious 200 206 208 + 9999988 palindromic 515 535 626 + 8997998 pancake 326 1712 1892 + 9974812 pandigital 894 898 1070 + 9998058 partition 5604 12310 75175 + 8118264 pentagonal 532 1335 1926 + 9983310 pernicious 200 206 208 + 9999988 Perrin 1130 3480 4610 + 6900995 plaindrome 1134 1135 1136 + 8888888 Poulet 11305 74665 223345 + 9816465 power 324 512 625 + 10000000 powerful 200 324 512 + 10000000 practical 200 204 208 + 10000000 prim.abundant 532 534 894 + 9999892 primorial 30030 510510 9699690 pronic 1260 1332 1640 + 9995082 Proth 1345 2945 3265 + 9990145 pseudoperfect 200 204 208 + 999996 repdigit 55555 66666 222222 + 8888888 repfigit 2580 3684 7385 + 694280 repunit 1464 3280 69905 + 9846355 Rhonda 15698 25284 53742 + 9892552 Ruth-Aaron 1330 1682 2108 + 9997416 Saint-Exupery 2040 12180 16320 + 9982500 Sastry 328 self 512 514 536 + 9999965 semiprime 206 326 514 + 9999965 sliding 200 1330 6410 + 9775865 Smith 535 895 1642 + 9999895 sphenic 322 518 530 + 9999985 square 324 625 1764 + 9972964 straight-line 840 5678 7654 + 8888888 strobogrammatic 9116 80008 86098 + 9998666 subfactorial 1854 super Niven 200 204 510 + 10000000 super-d 1070 1072 1145 + 9999895 superabundant 840 1260 1680 + 8648640 tau 204 328 516 + 10000000 taxicab 4104 171288 513856 + 9560896 tetrahedral 1140 1330 4060 + 9886435 tetranacci 208 39648 1055026 + 7555935 triangular 325 2485 3240 + 9997156 tribonacci 5768 66012 121415 trimorphic 624 625 90624 + 7890625 uban 1000010 1000012 1000015 + 10000000 Ulam 206 324 624 + 9999960 undulating 515 535 626 + 8989898 untouchable 206 322 324 + 999996 upside-down 2198 2828 4196 + 8965412 vampire 1260 102510 104260 + 939658 wasteful 200 204 206 + 9999988 weird 4030 10570 13370 + 994490 Wieferich 6161805 Woodall 895 106495 177146 + 5764800 Zeisel 54205 114985 448585 + 8712985 Zuckerman 624 1332 1344 + 9618912 Zumkeller 204 208 320 + 99948 zygodrome 1144 5544 6622 + 9999988