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Block #309,320

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/13/2013, 1:22:46 PM Β· Difficulty 9.9948 Β· 6,486,670 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2224c9aa3bf1abe39f1c1b066ca7db4e1bffa61af9afb5fe2555bb1798373161
View on Chainz β†—

Height

#309,320

Difficulty

9.994785

Transactions

2

Size

3.88 KB

Version

2

Bits

09feaa43

Nonce

236,534

Timestamp

12/13/2013, 1:22:46 PM

Confirmations

6,486,670

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

53be77e07db9c5c7c727ba25569b871089615f5375e38c604ac0b553a59fb7ab
Transactions (2)
Coinbase29935dd477ff7a…26bd7dfde332de
1 in β†’ 1 out10.0500 XPM110 B
AeKNrjNj…1NEq95Ta
b8e1cc1124fcf1…1c3fb2186f2693
25 in β†’ 2 out5000.0100 XPM3.68 KB
Ae5WFHbn…gBo7rvHrAcyz5F3H…VkuP1AEU
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.

2.991 Γ— 10⁹⁴(95-digit number)
29910743082049161605…62638304984693023999
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.991 Γ— 10⁹⁴(95-digit number)
29910743082049161605…62638304984693023999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.982 Γ— 10⁹⁴(95-digit number)
59821486164098323210…25276609969386047999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.196 Γ— 10⁹⁡(96-digit number)
11964297232819664642…50553219938772095999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.392 Γ— 10⁹⁡(96-digit number)
23928594465639329284…01106439877544191999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.785 Γ— 10⁹⁡(96-digit number)
47857188931278658568…02212879755088383999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.571 Γ— 10⁹⁡(96-digit number)
95714377862557317137…04425759510176767999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.914 Γ— 10⁹⁢(97-digit number)
19142875572511463427…08851519020353535999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.828 Γ— 10⁹⁢(97-digit number)
38285751145022926854…17703038040707071999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.657 Γ— 10⁹⁢(97-digit number)
76571502290045853709…35406076081414143999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.531 Γ— 10⁹⁷(98-digit number)
15314300458009170741…70812152162828287999
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,612,016 XPMΒ·at block #6,795,989 Β· updates every 60s
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