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Block #211,732

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/15/2013, 9:03:42 PM Β· Difficulty 9.9172 Β· 6,615,374 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
73d295536142c8c332a722b6f2d883838661a4be8fbb9427e1340b281a19d732
View on Chainz β†—

Height

#211,732

Difficulty

9.917234

Transactions

1

Size

200 B

Version

2

Bits

09eacfda

Nonce

92,278

Timestamp

10/15/2013, 9:03:42 PM

Confirmations

6,615,374

Mined by

⛏️ P2SHAdJ389VWNSzfCFgacQtZyNnrWvE84w9dhb

Merkle Root

ffbf8c213ee21eea40d9557716e80a50e78ea19383550b26317adcce6afe0d8f
Transactions (1)
Coinbaseffbf8c213ee21e…7adcce6afe0d8f
1 in β†’ 1 out10.1500 XPM109 B
AdJ389VW…E84w9dhb
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.

4.355 Γ— 10⁹⁢(97-digit number)
43557129528351778743…86804955824138374401
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
4.355 Γ— 10⁹⁢(97-digit number)
43557129528351778743…86804955824138374401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.711 Γ— 10⁹⁢(97-digit number)
87114259056703557487…73609911648276748801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.742 Γ— 10⁹⁷(98-digit number)
17422851811340711497…47219823296553497601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.484 Γ— 10⁹⁷(98-digit number)
34845703622681422995…94439646593106995201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.969 Γ— 10⁹⁷(98-digit number)
69691407245362845990…88879293186213990401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.393 Γ— 10⁹⁸(99-digit number)
13938281449072569198…77758586372427980801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.787 Γ— 10⁹⁸(99-digit number)
27876562898145138396…55517172744855961601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.575 Γ— 10⁹⁸(99-digit number)
55753125796290276792…11034345489711923201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.115 Γ— 10⁹⁹(100-digit number)
11150625159258055358…22068690979423846401
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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