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Block #213,259

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/16/2013, 6:55:35 PM Β· Difficulty 9.9208 Β· 6,587,734 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
576f59e8b3fa5f04cd2ccf7b3a00758495a53fc0833462543601899ca84b6c30
View on Chainz β†—

Height

#213,259

Difficulty

9.920758

Transactions

1

Size

198 B

Version

2

Bits

09ebb6c6

Nonce

2,283

Timestamp

10/16/2013, 6:55:35 PM

Confirmations

6,587,734

Mined by

⛏️ P2SHAbJsT1MFiTkk7HZiVSZy3MgHLJpF3oUXHW

Merkle Root

2d5fd2d5d8e9c48d40ff69753fe9dea0c4c68a337a5efefa4601348c91fa408d
Transactions (1)
Coinbase2d5fd2d5d8e9c4…01348c91fa408d
1 in β†’ 1 out10.1500 XPM109 B
AbJsT1MF…pF3oUXHW
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.

7.248 Γ— 10⁹¹(92-digit number)
72484729750606280610…80081963955204629601
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
7.248 Γ— 10⁹¹(92-digit number)
72484729750606280610…80081963955204629601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.449 Γ— 10⁹²(93-digit number)
14496945950121256122…60163927910409259201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.899 Γ— 10⁹²(93-digit number)
28993891900242512244…20327855820818518401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.798 Γ— 10⁹²(93-digit number)
57987783800485024488…40655711641637036801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.159 Γ— 10⁹³(94-digit number)
11597556760097004897…81311423283274073601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.319 Γ— 10⁹³(94-digit number)
23195113520194009795…62622846566548147201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.639 Γ— 10⁹³(94-digit number)
46390227040388019590…25245693133096294401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.278 Γ— 10⁹³(94-digit number)
92780454080776039181…50491386266192588801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.855 Γ— 10⁹⁴(95-digit number)
18556090816155207836…00982772532385177601
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:57,652,004 XPMΒ·at block #6,800,992 Β· updates every 60s
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