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Block #307,070

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/12/2013, 9:33:09 AM Β· Difficulty 9.9941 Β· 6,509,100 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f434573d91de90e951bd12aaa6d7ad1df0ddb87566082d1c89876813fb4a86ba
View on Chainz β†—

Height

#307,070

Difficulty

9.994073

Transactions

1

Size

198 B

Version

2

Bits

09fe7b96

Nonce

33,725

Timestamp

12/12/2013, 9:33:09 AM

Confirmations

6,509,100

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

101c8987a9eee86efbae29aeb5f294690a3fba3ece01cea60af721f142795f9f
Transactions (1)
Coinbase101c8987a9eee8…f721f142795f9f
1 in β†’ 1 out10.0000 XPM110 B
AeKNrjNj…1NEq95Ta
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.

6.971 Γ— 10⁸⁸(89-digit number)
69714951749261179264…10417259103268393591
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
6.971 Γ— 10⁸⁸(89-digit number)
69714951749261179264…10417259103268393591
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.394 Γ— 10⁸⁹(90-digit number)
13942990349852235852…20834518206536787181
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.788 Γ— 10⁸⁹(90-digit number)
27885980699704471705…41669036413073574361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.577 Γ— 10⁸⁹(90-digit number)
55771961399408943411…83338072826147148721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.115 Γ— 10⁹⁰(91-digit number)
11154392279881788682…66676145652294297441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.230 Γ— 10⁹⁰(91-digit number)
22308784559763577364…33352291304588594881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.461 Γ— 10⁹⁰(91-digit number)
44617569119527154729…66704582609177189761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.923 Γ— 10⁹⁰(91-digit number)
89235138239054309458…33409165218354379521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.784 Γ— 10⁹¹(92-digit number)
17847027647810861891…66818330436708759041
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9

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
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