A217263 Composite numbers such that every concatenation of their prime factors is prime.

21, 33, 51, 63, 93, 111, 133, 177, 201, 219, 247, 253, 327, 411, 427, 549, 573, 589, 657, 679, 687, 763, 793, 813, 833, 889, 993, 1077, 1081, 1119, 1127, 1243, 1339, 1347, 1401, 1411, 1497, 1501, 1603, 1623, 1651, 1671, 1821, 1839, 1843, 1851, 1981, 2009, 2019

Offset: 1

Author

Dmitri Kamenetsky, Sep 29 2012

Keywords

• nonn
• base

Comments

The smallest term with 3 or more prime factors is 63 = 3*3*7 (see A217264).

The smallest term with 4 or more prime factors is 21249 = 3*3*3*787 (see A217265).

The smallest term with 5 or more prime factors is 146461 = 7*7*7*7*61.

There is no term under 10^8 with 6 or more prime factors.

The smallest term with 3 or more distinct prime factors is 3311 = 7*11*43 (see A180679).

There is no term under 10^8 with 4 or more distinct prime factors.

Examples

			21 is 3*7. Both 37 and 73 are prime, so 21 is in the sequence.
63 is 3*3*7. 337, 373 and 733 are all prime, so 63 is in the sequence.
		

Crossrefs

Cf. A217264, A217265, A180679, A181559. Related sequences: A105184, A019549 and A106582.