1681

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1681 < 1680 | 1682 >
All Numbers
1600	1601	1602	1603	1604	1605	1606	1607	1608	1609
1610	1611	1612	1613	1614	1615	1616	1617	1618	1619
1620	1621	1622	1623	1624	1625	1626	1627	1628	1629
1630	1631	1632	1633	1634	1635	1636	1637	1638	1639
1640	1641	1642	1643	1644	1645	1646	1647	1648	1649
1650	1651	1652	1653	1654	1655	1656	1657	1658	1659
1660	1661	1662	1663	1664	1665	1666	1667	1668	1669
1670	1671	1672	1673	1674	1675	1676	1677	1678	1679
1680	1681	1682	1683	1684	1685	1686	1687	1688	1689
1690	1691	1692	1693	1694	1695	1696	1697	1698	1699

1681 is the number following 1680 and preceding 1682.

Properties

• Its factors are 1, 41 and 1681, making it a composite number. It is also a cubefree number.
• 1681 is an odd number .
• 1681 is an unhappy number.
  

• 1681 is a centered octagonal number.
  
• 1681 is deficient.
  
• Its prime factorization is 41².
  
• It is the first counterexample of the Euler's prime-generating polynomial \(x^2 + x + 41\), in which x = 40, in which smaller values of x produce prime numbers.

Approximations

Notation	Lower bound	Upper bound
Up-arrow notation	41 ↑ 2
Scientific notation	1.681 x 103	1.682 x 103
Slow-growing hierarchy	\(g_{\omega^{\omega}}(4)\)	\(g_{\omega^{\omega}}(5)\)
Copy notation	16[2]	17[2]
Chained arrow notation	41 → 2
Bowers' Exploding Array Function/Bird's array notation	{41,2}
Fast-growing hierarchy	f2(7)	f2(8)
Hardy hierarchy	Hω(840)	Hω(841)
Middle-growing hierarchy	m(ω,10)	m(ω,11)
Hyper-E notation	E3.2256
Hyper-E notation (non-10 base)	\(E[41]2\)
Hyperfactorial array notation	6!	7!
X-Sequence Hyper-Exponential Notation	41{1}2
Steinhaus-Moser Notation	4[3]	5[3]
PlantStar's Debut Notation	[1]	[2]
H* function	H(0)	H(0.1)
Bashicu matrix system with respect to version 4	(0)[41]	(0)[41]
m(n) map	m(1)(4)	m(1)(5)
s(n) map	\(s(1)(\lambda x . x+1)(839)\)	\(s(1)(\lambda x . x+1)(840)\)