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Block #211,497

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/15/2013, 5:58:24 PM Β· Difficulty 9.9164 Β· 6,606,119 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
91d84a177e102d81c8ef8221978faa28a637fe26a707eaac9b80fb9d28f88af8
View on Chainz β†—

Height

#211,497

Difficulty

9.916409

Transactions

2

Size

4.97 KB

Version

2

Bits

09ea99cf

Nonce

47,714

Timestamp

10/15/2013, 5:58:24 PM

Confirmations

6,606,119

Mined by

⛏️ P2SHAVQtj9szcPSbXf2Kn31DQ2okAd4P34aCDq

Merkle Root

7d724adb7132d6e046ae62672053587bed6a9565b1b1c54b18d6b148326fdad4
Transactions (2)
Coinbasec090e1b964d59e…8257af23f17fdc
1 in β†’ 1 out10.2000 XPM109 B
AVQtj9sz…4P34aCDq
2f9330ae9e2908…d8ff55d722eb77
41 in β†’ 2 out385.0141 XPM4.78 KB
AGEBmx77…rXF6mZuAAZShbq4V…riUG96zQ
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.

1.969 Γ— 10⁹⁴(95-digit number)
19691892022071289984…27262429233966741001
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
1.969 Γ— 10⁹⁴(95-digit number)
19691892022071289984…27262429233966741001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.938 Γ— 10⁹⁴(95-digit number)
39383784044142579969…54524858467933482001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.876 Γ— 10⁹⁴(95-digit number)
78767568088285159939…09049716935866964001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.575 Γ— 10⁹⁡(96-digit number)
15753513617657031987…18099433871733928001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.150 Γ— 10⁹⁡(96-digit number)
31507027235314063975…36198867743467856001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.301 Γ— 10⁹⁡(96-digit number)
63014054470628127951…72397735486935712001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.260 Γ— 10⁹⁢(97-digit number)
12602810894125625590…44795470973871424001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.520 Γ— 10⁹⁢(97-digit number)
25205621788251251180…89590941947742848001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.041 Γ— 10⁹⁢(97-digit number)
50411243576502502361…79181883895485696001
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:57,784,985 XPMΒ·at block #6,817,615 Β· updates every 60s
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