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Block #227,119

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/25/2013, 4:28:27 PM Β· Difficulty 9.9363 Β· 6,576,436 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4e9903a959d37707f25808e932969b066847ded7aa682fbad80ac75fb4d7cdee
View on Chainz β†—

Height

#227,119

Difficulty

9.936304

Transactions

1

Size

199 B

Version

2

Bits

09efb199

Nonce

57,243

Timestamp

10/25/2013, 4:28:27 PM

Confirmations

6,576,436

Mined by

⛏️ wAHPLSWVdVVmfZ1Mw8oxTBdXzN3ZdicvSUu

Merkle Root

145ed56738a1b9a3c49f7aeb9f740f6c3cdbcec30ad06f2dd7a4e33ece581729
Transactions (1)
Coinbase145ed56738a1b9…a4e33ece581729
1 in β†’ 1 out10.1100 XPM109 B
AHPLSWVd…ZdicvSUu
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.

3.736 Γ— 10⁹³(94-digit number)
37360405893200200173…72927272822526558641
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
3.736 Γ— 10⁹³(94-digit number)
37360405893200200173…72927272822526558641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.472 Γ— 10⁹³(94-digit number)
74720811786400400347…45854545645053117281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.494 Γ— 10⁹⁴(95-digit number)
14944162357280080069…91709091290106234561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.988 Γ— 10⁹⁴(95-digit number)
29888324714560160138…83418182580212469121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.977 Γ— 10⁹⁴(95-digit number)
59776649429120320277…66836365160424938241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.195 Γ— 10⁹⁡(96-digit number)
11955329885824064055…33672730320849876481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.391 Γ— 10⁹⁡(96-digit number)
23910659771648128111…67345460641699752961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.782 Γ— 10⁹⁡(96-digit number)
47821319543296256222…34690921283399505921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.564 Γ— 10⁹⁡(96-digit number)
95642639086592512444…69381842566799011841
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:57,672,472 XPMΒ·at block #6,803,554 Β· updates every 60s
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