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Block #211,287

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/15/2013, 3:36:09 PM Β· Difficulty 9.9152 Β· 6,606,646 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c063525bb4c8a9f5b0cd6c06e9e987cc2e6f082f962714886c8dbc4e9ae26feb
View on Chainz β†—

Height

#211,287

Difficulty

9.915247

Transactions

1

Size

199 B

Version

2

Bits

09ea4da7

Nonce

17,292

Timestamp

10/15/2013, 3:36:09 PM

Confirmations

6,606,646

Mined by

⛏️ P2SHAJ9ygF5Kz2CrinFn4YPC5hpP7itVQ23kYY

Merkle Root

41c4ed76fb1299647ad4c0583e906326fc544dc695811246fbea1c4c0e76e0f1
Transactions (1)
Coinbase41c4ed76fb1299…ea1c4c0e76e0f1
1 in β†’ 1 out10.1600 XPM109 B
AJ9ygF5K…tVQ23kYY
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.

7.826 Γ— 10⁹³(94-digit number)
78264267303853583731…36024816287432825201
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
7.826 Γ— 10⁹³(94-digit number)
78264267303853583731…36024816287432825201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.565 Γ— 10⁹⁴(95-digit number)
15652853460770716746…72049632574865650401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.130 Γ— 10⁹⁴(95-digit number)
31305706921541433492…44099265149731300801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.261 Γ— 10⁹⁴(95-digit number)
62611413843082866985…88198530299462601601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.252 Γ— 10⁹⁡(96-digit number)
12522282768616573397…76397060598925203201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.504 Γ— 10⁹⁡(96-digit number)
25044565537233146794…52794121197850406401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.008 Γ— 10⁹⁡(96-digit number)
50089131074466293588…05588242395700812801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.001 Γ— 10⁹⁢(97-digit number)
10017826214893258717…11176484791401625601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.003 Γ— 10⁹⁢(97-digit number)
20035652429786517435…22352969582803251201
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:57,787,529 XPMΒ·at block #6,817,932 Β· updates every 60s
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