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Block #1,319,718

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/9/2015, 11:22:30 AM Β· Difficulty 10.8606 Β· 5,496,978 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
66a693a574b2b4b6712d383df06acd12c2448b01ce2a31c808d9294f8f38b7a5
View on Chainz β†—

Height

#1,319,718

Difficulty

10.860618

Transactions

2

Size

20.07 KB

Version

2

Bits

0adc516e

Nonce

288,600,837

Timestamp

11/9/2015, 11:22:30 AM

Confirmations

5,496,978

Mined by

⛏️ P2SHAZocfDh6QaEvysqcHubQwiqNjYKWVyuiPW

Merkle Root

8124799e459aae3db792f6f3c4b06c23e1521c4b62089d5f5ceaa6e1e6b59a1c
Transactions (2)
Coinbasefde8d3af52659a…3ac1d32779612e
1 in β†’ 1 out8.6800 XPM110 B
AZocfDh6…KWVyuiPW
899eca4772782f…df6cf013313622
137 in β†’ 2 out1816.8700 XPM19.87 KB
AHNccZy4…RwZSfQd3AcEbwGa9…au9KL6TC
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.

3.660 Γ— 10⁹⁡(96-digit number)
36600520218355837705…26318660865194350721
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
3.660 Γ— 10⁹⁡(96-digit number)
36600520218355837705…26318660865194350721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.320 Γ— 10⁹⁡(96-digit number)
73201040436711675410…52637321730388701441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.464 Γ— 10⁹⁢(97-digit number)
14640208087342335082…05274643460777402881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.928 Γ— 10⁹⁢(97-digit number)
29280416174684670164…10549286921554805761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.856 Γ— 10⁹⁢(97-digit number)
58560832349369340328…21098573843109611521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.171 Γ— 10⁹⁷(98-digit number)
11712166469873868065…42197147686219223041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.342 Γ— 10⁹⁷(98-digit number)
23424332939747736131…84394295372438446081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.684 Γ— 10⁹⁷(98-digit number)
46848665879495472262…68788590744876892161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.369 Γ— 10⁹⁷(98-digit number)
93697331758990944525…37577181489753784321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.873 Γ— 10⁹⁸(99-digit number)
18739466351798188905…75154362979507568641
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
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