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Block #125,175

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/20/2013, 2:14:38 AM Β· Difficulty 9.7757 Β· 6,700,190 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ff3556b8168a2fc83083869013e87be14eda0274dbc1378f0858618dddfda311
View on Chainz β†—

Height

#125,175

Difficulty

9.775696

Transactions

1

Size

200 B

Version

2

Bits

09c69400

Nonce

374,070

Timestamp

8/20/2013, 2:14:38 AM

Confirmations

6,700,190

Mined by

⛏️ P2SHAKaGDwVVv7VLKh2cmLacAjw2bVh5Bk5GFu

Merkle Root

66802c61c966468d453d5925efb06ac0fc4921ef7947560440f4a2e1050c0a50
Transactions (1)
Coinbase66802c61c96646…f4a2e1050c0a50
1 in β†’ 1 out10.4500 XPM109 B
AKaGDwVV…h5Bk5GFu
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.

2.275 Γ— 10⁹⁸(99-digit number)
22754073435816623003…02137897488338789561
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
2.275 Γ— 10⁹⁸(99-digit number)
22754073435816623003…02137897488338789561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.550 Γ— 10⁹⁸(99-digit number)
45508146871633246006…04275794976677579121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.101 Γ— 10⁹⁸(99-digit number)
91016293743266492012…08551589953355158241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.820 Γ— 10⁹⁹(100-digit number)
18203258748653298402…17103179906710316481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.640 Γ— 10⁹⁹(100-digit number)
36406517497306596805…34206359813420632961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.281 Γ— 10⁹⁹(100-digit number)
72813034994613193610…68412719626841265921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.456 Γ— 10¹⁰⁰(101-digit number)
14562606998922638722…36825439253682531841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.912 Γ— 10¹⁰⁰(101-digit number)
29125213997845277444…73650878507365063681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.825 Γ— 10¹⁰⁰(101-digit number)
58250427995690554888…47301757014730127361
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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