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Block #1,822,246

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/24/2016, 4:42:02 AM Β· Difficulty 10.8398 Β· 5,004,604 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
df471789ed88d5e97a83ccea2d9704e46da4d6b93ed6cac0ffe5fb4d6a1cf2d9
View on Chainz β†—

Height

#1,822,246

Difficulty

10.839801

Transactions

1

Size

242 B

Version

2

Bits

0ad6fd39

Nonce

196,418,354

Timestamp

10/24/2016, 4:42:02 AM

Confirmations

5,004,604

Mined by

⛏️ P2SHATd5Bq5SNppozp9HDzLQKxc4KVPcfPgHVj

Merkle Root

fbe3763f43b8e7d0cb7059b2826d9f378bf5a7d6ab854f6c7bdf7acfc0ee9d22
Transactions (1)
Coinbasefbe3763f43b8e7…df7acfc0ee9d22
1 in β†’ 2 out8.5000 XPM152 B
ATd5Bq5S…PcfPgHVjALPu3s2c…EJXLjVFh
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.574 Γ— 10⁹⁡(96-digit number)
25740591582449653261…64727581137169821721
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
2.574 Γ— 10⁹⁡(96-digit number)
25740591582449653261…64727581137169821721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.148 Γ— 10⁹⁡(96-digit number)
51481183164899306522…29455162274339643441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.029 Γ— 10⁹⁢(97-digit number)
10296236632979861304…58910324548679286881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.059 Γ— 10⁹⁢(97-digit number)
20592473265959722609…17820649097358573761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.118 Γ— 10⁹⁢(97-digit number)
41184946531919445218…35641298194717147521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.236 Γ— 10⁹⁢(97-digit number)
82369893063838890436…71282596389434295041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.647 Γ— 10⁹⁷(98-digit number)
16473978612767778087…42565192778868590081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.294 Γ— 10⁹⁷(98-digit number)
32947957225535556174…85130385557737180161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.589 Γ— 10⁹⁷(98-digit number)
65895914451071112349…70260771115474360321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.317 Γ— 10⁹⁸(99-digit number)
13179182890214222469…40521542230948720641
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,858,967 XPMΒ·at block #6,826,849 Β· updates every 60s
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