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Block #171,493

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/19/2013, 1:02:15 PM Β· Difficulty 9.8643 Β· 6,630,748 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2b9bf8037e6c77af552b6797d53b8e82b49adaec263e2dcce307fecaeb11ff2a
View on Chainz β†—

Height

#171,493

Difficulty

9.864333

Transactions

1

Size

197 B

Version

2

Bits

09dd44ea

Nonce

87,337

Timestamp

9/19/2013, 1:02:15 PM

Confirmations

6,630,748

Mined by

⛏️ P2SHAPbne1gSsQ4A6bqfDhiLcmWiENFS5g2nZv

Merkle Root

deb4cf891f60f12b487c62ec3a8bc39f3f90e6958d9b0f365f6e1dee3d1c6416
Transactions (1)
Coinbasedeb4cf891f60f1…6e1dee3d1c6416
1 in β†’ 1 out10.2600 XPM109 B
APbne1gS…FS5g2nZv
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.

4.316 Γ— 10⁹⁰(91-digit number)
43161631831509934844…36506888557988206081
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
4.316 Γ— 10⁹⁰(91-digit number)
43161631831509934844…36506888557988206081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.632 Γ— 10⁹⁰(91-digit number)
86323263663019869689…73013777115976412161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.726 Γ— 10⁹¹(92-digit number)
17264652732603973937…46027554231952824321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.452 Γ— 10⁹¹(92-digit number)
34529305465207947875…92055108463905648641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.905 Γ— 10⁹¹(92-digit number)
69058610930415895751…84110216927811297281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.381 Γ— 10⁹²(93-digit number)
13811722186083179150…68220433855622594561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.762 Γ— 10⁹²(93-digit number)
27623444372166358300…36440867711245189121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.524 Γ— 10⁹²(93-digit number)
55246888744332716600…72881735422490378241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.104 Γ— 10⁹³(94-digit number)
11049377748866543320…45763470844980756481
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:57,661,937 XPMΒ·at block #6,802,240 Β· updates every 60s
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