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Block #34,589

2CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/14/2013, 6:44:24 AM Β· Difficulty 7.9935 Β· 6,774,280 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
307d7cde4f1ab528651fe829d9ac57c4b2eeea001603e87275c36006da91fab8
View on Chainz β†—

Height

#34,589

Difficulty

7.993470

Transactions

1

Size

200 B

Version

2

Bits

07fe540f

Nonce

307

Timestamp

7/14/2013, 6:44:24 AM

Confirmations

6,774,280

Mined by

⛏️ P2SHAKsLKPc8KMAFsNueJDJSs3dfp1zkBgUqcr

Merkle Root

c4b9851d22ca158246609df2094169eca87201c3f64b61d1f1cde27de988e3aa
Transactions (1)
Coinbasec4b9851d22ca15…cde27de988e3aa
1 in β†’ 1 out15.6300 XPM109 B
AKsLKPc8…zkBgUqcr
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.

7.171 Γ— 10⁹⁷(98-digit number)
71711328646799474845…01535379071804112961
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
7.171 Γ— 10⁹⁷(98-digit number)
71711328646799474845…01535379071804112961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.434 Γ— 10⁹⁸(99-digit number)
14342265729359894969…03070758143608225921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.868 Γ— 10⁹⁸(99-digit number)
28684531458719789938…06141516287216451841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.736 Γ— 10⁹⁸(99-digit number)
57369062917439579876…12283032574432903681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.147 Γ— 10⁹⁹(100-digit number)
11473812583487915975…24566065148865807361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.294 Γ— 10⁹⁹(100-digit number)
22947625166975831950…49132130297731614721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.589 Γ— 10⁹⁹(100-digit number)
45895250333951663901…98264260595463229441
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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
CommonChain length 7

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,715,002 XPMΒ·at block #6,808,868 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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