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Block #167,363

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/16/2013, 1:26:13 PM Β· Difficulty 9.8685 Β· 6,648,942 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9f3c4ecd0648bc5f651dca13190c6b328e7b7777524ce1522a4b5048995c3538
View on Chainz β†—

Height

#167,363

Difficulty

9.868467

Transactions

1

Size

199 B

Version

2

Bits

09de53d9

Nonce

125,360

Timestamp

9/16/2013, 1:26:13 PM

Confirmations

6,648,942

Mined by

⛏️ P2SHAe6PYBDNs6MFPfqSfG8TyUUBAHjSQhB18y

Merkle Root

3d01e20093064a29f423f3d10f149668b736c1263327cd4c1bd16d8bd8786ba8
Transactions (1)
Coinbase3d01e20093064a…d16d8bd8786ba8
1 in β†’ 1 out10.2500 XPM109 B
Ae6PYBDN…jSQhB18y
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.

1.251 Γ— 10⁹⁡(96-digit number)
12512532674665053799…65676656718760001919
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
1.251 Γ— 10⁹⁡(96-digit number)
12512532674665053799…65676656718760001919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.502 Γ— 10⁹⁡(96-digit number)
25025065349330107598…31353313437520003839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.005 Γ— 10⁹⁡(96-digit number)
50050130698660215196…62706626875040007679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.001 Γ— 10⁹⁢(97-digit number)
10010026139732043039…25413253750080015359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.002 Γ— 10⁹⁢(97-digit number)
20020052279464086078…50826507500160030719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.004 Γ— 10⁹⁢(97-digit number)
40040104558928172156…01653015000320061439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.008 Γ— 10⁹⁢(97-digit number)
80080209117856344313…03306030000640122879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.601 Γ— 10⁹⁷(98-digit number)
16016041823571268862…06612060001280245759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.203 Γ— 10⁹⁷(98-digit number)
32032083647142537725…13224120002560491519
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 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
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
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