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Block #311,741

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/14/2013, 5:04:49 PM Β· Difficulty 9.9956 Β· 6,491,715 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2cfa18108f47cfade26334f9ed5de082552c419ca640c393a612317ad8ec252d
View on Chainz β†—

Height

#311,741

Difficulty

9.995583

Transactions

2

Size

720 B

Version

2

Bits

09fede8a

Nonce

5,353

Timestamp

12/14/2013, 5:04:49 PM

Confirmations

6,491,715

Mined by

⛏️ P2SHAFu8F1JKgtt3NEkXoDdNwgp3GUf89wZmxg

Merkle Root

21b4710e84afbdf9d57ed8ecde07d0df61f622af663c1935ff4549fa3e153b4d
Transactions (2)
Coinbase25cb811950e3d1…4bea39c2dc323b
1 in β†’ 1 out10.0000 XPM109 B
AFu8F1JK…f89wZmxg
8bff527bbdcc34…c1a1d2fc1eb4e5
3 in β†’ 2 out29.9305 XPM520 B
AHLpjtpx…5qvnLUxzAXWxPH3m…yp39ud8w
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.

3.692 Γ— 10⁹⁢(97-digit number)
36925734473802697901…96724278329925617921
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
3.692 Γ— 10⁹⁢(97-digit number)
36925734473802697901…96724278329925617921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.385 Γ— 10⁹⁢(97-digit number)
73851468947605395802…93448556659851235841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.477 Γ— 10⁹⁷(98-digit number)
14770293789521079160…86897113319702471681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.954 Γ— 10⁹⁷(98-digit number)
29540587579042158321…73794226639404943361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.908 Γ— 10⁹⁷(98-digit number)
59081175158084316642…47588453278809886721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.181 Γ— 10⁹⁸(99-digit number)
11816235031616863328…95176906557619773441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.363 Γ— 10⁹⁸(99-digit number)
23632470063233726656…90353813115239546881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.726 Γ— 10⁹⁸(99-digit number)
47264940126467453313…80707626230479093761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.452 Γ— 10⁹⁸(99-digit number)
94529880252934906627…61415252460958187521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.890 Γ— 10⁹⁹(100-digit number)
18905976050586981325…22830504921916375041
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:57,671,675 XPMΒ·at block #6,803,455 Β· updates every 60s
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