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Block #173,102

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/20/2013, 5:51:44 PM Β· Difficulty 9.8612 Β· 6,622,807 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ddd1e88e9c84c2bf00543ff0f0babb6fdb0eef48872a4bdaeafe82bf3a0caa12
View on Chainz β†—

Height

#173,102

Difficulty

9.861189

Transactions

2

Size

3.56 KB

Version

2

Bits

09dc76df

Nonce

10,536

Timestamp

9/20/2013, 5:51:44 PM

Confirmations

6,622,807

Mined by

⛏️ P2SHAJQ7bqzh8jMKwbhminzZ7vurTxoY2ANRaW

Merkle Root

fc689e9b86b6fdd086e6b3e20c64697fdc8d3873a8dff118a5170af442600be7
Transactions (2)
Coinbase8ba780e6bcee0a…73f269d7448124
1 in β†’ 1 out10.3100 XPM109 B
AJQ7bqzh…oY2ANRaW
fe0c2e0c247997…57c715d50cbb8b
23 in β†’ 1 out43.8931 XPM3.37 KB
AS6wjyQC…E2BfJdMN
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.

3.913 Γ— 10⁹³(94-digit number)
39134685559353951118…16605294922724920961
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
3.913 Γ— 10⁹³(94-digit number)
39134685559353951118…16605294922724920961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.826 Γ— 10⁹³(94-digit number)
78269371118707902237…33210589845449841921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.565 Γ— 10⁹⁴(95-digit number)
15653874223741580447…66421179690899683841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.130 Γ— 10⁹⁴(95-digit number)
31307748447483160895…32842359381799367681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.261 Γ— 10⁹⁴(95-digit number)
62615496894966321790…65684718763598735361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.252 Γ— 10⁹⁡(96-digit number)
12523099378993264358…31369437527197470721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.504 Γ— 10⁹⁡(96-digit number)
25046198757986528716…62738875054394941441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.009 Γ— 10⁹⁡(96-digit number)
50092397515973057432…25477750108789882881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.001 Γ— 10⁹⁢(97-digit number)
10018479503194611486…50955500217579765761
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:57,611,357 XPMΒ·at block #6,795,908 Β· updates every 60s
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