Today, having turned 27181 days old and also 3883 weeks old, I discovered that 27181 is a very special number indeed. It is a sphenic number with the property that when its three prime factors are concatenated in any order, the resultant numbers are all prime. The details are as follows:$$27181=7 \times 11 \times 353\\ \text{with the concatenated numbers thus being}\\711353, 735311, 117353, 113537, 353711, 353117$$In my long journey to this numbered day, there has only been one previous numbered day and that was 3311. Its details are as follows:$$3311=7 \times 11 \times 43\\\text{with the concatenated numbers thus being}\\71143, 74311, 11743, 11437, 43711, 43117$$In my long journey from womb to tomb, I'm only likely to encounter one further such numbered day and that is 32153. Its details are:$$ 32153=11 \times 37 \times 79\\ \text{with the concatenated numbers thus being}\\113779, 117937, 371179, 377911, 791137, 793711$$That numbered day falls on Tuesday, April 14th 2037 and I may or may not make it that far. It is shortly after my 88th birthday.
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| My special sphenic numbers are 3311, 27181 and 32153 |
The other numbers up to one million are 41237, 53977, 86507, 110971, 125069, 208579, 256413, 500981, 543337, 853811, 901949 and 964481. The OEIS comments state that, for quadruply composite numbers, is no term with four distinct prime factors under one hundred million.
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