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Block #204,459

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/11/2013, 12:33:28 PM Β· Difficulty 9.8986 Β· 6,612,684 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
46338439ce4b4fa8f8a4417b11b0dbc46e0ab9f1a6bad8b5a714dd9a218f8ae7
View on Chainz β†—

Height

#204,459

Difficulty

9.898582

Transactions

1

Size

198 B

Version

2

Bits

09e6097b

Nonce

252,475

Timestamp

10/11/2013, 12:33:28 PM

Confirmations

6,612,684

Mined by

⛏️ P2SHAHNdTz9RdyhMpsaRttP7HwiXvgDHU2jpcA

Merkle Root

6a82092b415aaa08bfee3477f042abafc0df7d033d616b2136f887d5b3c646e4
Transactions (1)
Coinbase6a82092b415aaa…f887d5b3c646e4
1 in β†’ 1 out10.1900 XPM109 B
AHNdTz9R…DHU2jpcA
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.

9.374 Γ— 10⁹²(93-digit number)
93740917496277433819…12552042650056952001
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
9.374 Γ— 10⁹²(93-digit number)
93740917496277433819…12552042650056952001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.874 Γ— 10⁹³(94-digit number)
18748183499255486763…25104085300113904001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.749 Γ— 10⁹³(94-digit number)
37496366998510973527…50208170600227808001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.499 Γ— 10⁹³(94-digit number)
74992733997021947055…00416341200455616001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.499 Γ— 10⁹⁴(95-digit number)
14998546799404389411…00832682400911232001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.999 Γ— 10⁹⁴(95-digit number)
29997093598808778822…01665364801822464001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.999 Γ— 10⁹⁴(95-digit number)
59994187197617557644…03330729603644928001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.199 Γ— 10⁹⁡(96-digit number)
11998837439523511528…06661459207289856001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.399 Γ— 10⁹⁡(96-digit number)
23997674879047023057…13322918414579712001
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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