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Block #227,762

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/26/2013, 2:08:19 AM Β· Difficulty 9.9372 Β· 6,571,158 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f64ed30cd3024b5b35ebcbb5a9ce7aa334afd5c3af020241801ac66e901c7557
View on Chainz β†—

Height

#227,762

Difficulty

9.937196

Transactions

2

Size

540 B

Version

2

Bits

09efec14

Nonce

150,235

Timestamp

10/26/2013, 2:08:19 AM

Confirmations

6,571,158

Mined by

⛏️ P2SHAdrYVTm6tX9eRqNDg18gVHTNxMUkrsrMvD

Merkle Root

76fd3a9c6bc5d8c92f48519d019ad24c57c259d9b0154460b29bb1a3c425dbbb
Transactions (2)
Coinbase68e7eea4a95b7e…8fc862368a1a10
1 in β†’ 1 out10.1200 XPM109 B
AdrYVTm6…UkrsrMvD
d092a093a80683…cc13acad90b077
2 in β†’ 1 out30.3100 XPM341 B
AbEVNHvT…4XP8UPJZ
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.

5.444 Γ— 10⁹³(94-digit number)
54440576076558965480…38898528807446909441
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
5.444 Γ— 10⁹³(94-digit number)
54440576076558965480…38898528807446909441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.088 Γ— 10⁹⁴(95-digit number)
10888115215311793096…77797057614893818881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.177 Γ— 10⁹⁴(95-digit number)
21776230430623586192…55594115229787637761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.355 Γ— 10⁹⁴(95-digit number)
43552460861247172384…11188230459575275521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.710 Γ— 10⁹⁴(95-digit number)
87104921722494344769…22376460919150551041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.742 Γ— 10⁹⁡(96-digit number)
17420984344498868953…44752921838301102081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.484 Γ— 10⁹⁡(96-digit number)
34841968688997737907…89505843676602204161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.968 Γ— 10⁹⁡(96-digit number)
69683937377995475815…79011687353204408321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.393 Γ— 10⁹⁢(97-digit number)
13936787475599095163…58023374706408816641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.787 Γ— 10⁹⁢(97-digit number)
27873574951198190326…16046749412817633281
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,635,392 XPMΒ·at block #6,798,919 Β· updates every 60s
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