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Block #274,625

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/26/2013, 8:57:28 AM Β· Difficulty 9.9581 Β· 6,529,262 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ecf1ca4ac49304d0f9cf4e840f9d5af3ed039e5628b7dea6374f275531317ce5
View on Chainz β†—

Height

#274,625

Difficulty

9.958149

Transactions

1

Size

198 B

Version

2

Bits

09f5493f

Nonce

2,595

Timestamp

11/26/2013, 8:57:28 AM

Confirmations

6,529,262

Mined by

⛏️ P2SHAR1c6GU1LfcTC2hHVwEhQzfgCyzzkggCDv

Merkle Root

f85be5c666bef3bc623ecb090a6b99f3bb90f9fc4e6fbbfa999c2cfdc77da2b9
Transactions (1)
Coinbasef85be5c666bef3…9c2cfdc77da2b9
1 in β†’ 1 out10.0700 XPM109 B
AR1c6GU1…zzkggCDv
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.

1.148 Γ— 10⁹¹(92-digit number)
11481853603999584455…92643185165720638401
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
1.148 Γ— 10⁹¹(92-digit number)
11481853603999584455…92643185165720638401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.296 Γ— 10⁹¹(92-digit number)
22963707207999168910…85286370331441276801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.592 Γ— 10⁹¹(92-digit number)
45927414415998337820…70572740662882553601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.185 Γ— 10⁹¹(92-digit number)
91854828831996675641…41145481325765107201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.837 Γ— 10⁹²(93-digit number)
18370965766399335128…82290962651530214401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.674 Γ— 10⁹²(93-digit number)
36741931532798670256…64581925303060428801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.348 Γ— 10⁹²(93-digit number)
73483863065597340512…29163850606120857601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.469 Γ— 10⁹³(94-digit number)
14696772613119468102…58327701212241715201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.939 Γ— 10⁹³(94-digit number)
29393545226238936205…16655402424483430401
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:57,675,140 XPMΒ·at block #6,803,886 Β· updates every 60s
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