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INTANGIBLE ASSETS: | 12 Months Ended
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Dec. 31, 2022
INTANGIBLE ASSETS: |
INTANGIBLE ASSETS: | ​ NOTE 6—INTANGIBLE ASSETS: ​
​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | At December 31,
(in millions) |  | 2022 |  | 2021
Mining concessions | ​ | $ | 121.2 | ​ | $ | 121.2
Mine engineering and development studies | ​ |  | 19.8 | ​ |  | 19.8
Software | ​ |  | 70.3 | ​ |  | 65.4
​ | ​ |  | 211.3 | ​ |  | 206.4
Accumulated amortization: | ​ |  | ​ | ​ | ​ | ​
Mining concessions | ​ | ​ | (42.2) | ​ | ​ | (40.4)
Mine engineering and development studies | ​ | ​ | (19.2) | ​ | ​ | (18.2)
Software | ​ | ​ | (57.1) | ​ | ​ | (51.6)
​ | ​ | ​ | (118.5) | ​ | ​ | (110.2)
Goodwill | ​ |  | 41.9 | ​ |  | 41.9
Intangible assets, net | ​ | $ | 134.7 | ​ | $ | 138.1
​ Amortization of intangibles for the years ended December 31, 2022, 2021 and 2020, amounted to $7.3 million, $8.7 million and $9.2 million, respectively. Estimated amortization is as follows: ​
​ | ​ | ​ | ​
Estimated amortization expense (in millions): |  | ​ | ​
2023 | ​ | $ | 6.9
2024 | ​ | ​ | 5.8
2025 | ​ | ​ | 5.1
2026 | ​ | ​ | 1.8
2027 | ​ | ​ | 1.8
Total 2023 - 2027 | ​ | $ | 21.4
Average annual | ​ | $ | 4.3
​ Goodwill includes $17.0 million generated in 1997 as a result of purchasing a third party interest in the Buenavista mine. It also includes $24.9 million representing the amount of the purchase price in excess of the fair value of the net assets acquired from El Pilar mine. This goodwill is attributable to future benefits that the Company expects to realize from the mine and will not be deductible for income tax purposes.

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- Definition The entire disclosure for goodwill and intangible assets. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 350 -URI https://asc.fasb.org/topic&trid=2144416 + Details
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