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Block #2,284,639

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/6/2017, 8:13:58 AM Β· Difficulty 10.9551 Β· 4,546,478 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
efe8bd57ad17e5ca9b047926114d99ff675c5fa5ab07654a7e56ff7ff0cb01a3
View on Chainz β†—

Height

#2,284,639

Difficulty

10.955134

Transactions

1

Size

200 B

Version

2

Bits

0af483ae

Nonce

347,868,622

Timestamp

9/6/2017, 8:13:58 AM

Confirmations

4,546,478

Mined by

⛏️ P2SHAHHrwT46Nt82FzEJdjVQQvnkcUtd86mEgg

Merkle Root

d374c1b774581baee984bc35436163cdc96910ad35422d0ab63c1589e02d011f
Transactions (1)
Coinbased374c1b774581b…3c1589e02d011f
1 in β†’ 1 out8.3200 XPM110 B
AHHrwT46…td86mEgg
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.

1.338 Γ— 10⁹⁴(95-digit number)
13383015466050193526…07927907319048245281
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
1.338 Γ— 10⁹⁴(95-digit number)
13383015466050193526…07927907319048245281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.676 Γ— 10⁹⁴(95-digit number)
26766030932100387053…15855814638096490561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.353 Γ— 10⁹⁴(95-digit number)
53532061864200774106…31711629276192981121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.070 Γ— 10⁹⁡(96-digit number)
10706412372840154821…63423258552385962241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.141 Γ— 10⁹⁡(96-digit number)
21412824745680309642…26846517104771924481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.282 Γ— 10⁹⁡(96-digit number)
42825649491360619285…53693034209543848961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.565 Γ— 10⁹⁡(96-digit number)
85651298982721238570…07386068419087697921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.713 Γ— 10⁹⁢(97-digit number)
17130259796544247714…14772136838175395841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.426 Γ— 10⁹⁢(97-digit number)
34260519593088495428…29544273676350791681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.852 Γ— 10⁹⁢(97-digit number)
68521039186176990856…59088547352701583361
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:57,893,081 XPMΒ·at block #6,831,116 Β· updates every 60s
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