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Block #185,683

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/29/2013, 11:16:59 AM Β· Difficulty 9.8628 Β· 6,619,129 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
67d43e4125e8801cbb4d35051736ef3de3bf3e94c10e260a1128b12f4534f03c
View on Chainz β†—

Height

#185,683

Difficulty

9.862771

Transactions

1

Size

198 B

Version

2

Bits

09dcde94

Nonce

7,445

Timestamp

9/29/2013, 11:16:59 AM

Confirmations

6,619,129

Mined by

⛏️ P2SHAWbQMT1UFX9Fb1nejhFo5DMbcK8Pt4ow7J

Merkle Root

7378882dd051435a28c2eb0d2e2a5e4ea0af0ab325639d326e6874da6789cab8
Transactions (1)
Coinbase7378882dd05143…6874da6789cab8
1 in β†’ 1 out10.2600 XPM109 B
AWbQMT1U…8Pt4ow7J
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.

2.240 Γ— 10⁹²(93-digit number)
22409171660061865744…95573075915520824021
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
2.240 Γ— 10⁹²(93-digit number)
22409171660061865744…95573075915520824021
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.481 Γ— 10⁹²(93-digit number)
44818343320123731488…91146151831041648041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.963 Γ— 10⁹²(93-digit number)
89636686640247462977…82292303662083296081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.792 Γ— 10⁹³(94-digit number)
17927337328049492595…64584607324166592161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.585 Γ— 10⁹³(94-digit number)
35854674656098985191…29169214648333184321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.170 Γ— 10⁹³(94-digit number)
71709349312197970382…58338429296666368641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.434 Γ— 10⁹⁴(95-digit number)
14341869862439594076…16676858593332737281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.868 Γ— 10⁹⁴(95-digit number)
28683739724879188152…33353717186665474561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.736 Γ— 10⁹⁴(95-digit number)
57367479449758376305…66707434373330949121
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
Circulating Supply:57,682,565 XPMΒ·at block #6,804,811 Β· updates every 60s
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