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Block #255,022

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/11/2013, 1:24:21 AM Β· Difficulty 9.9737 Β· 6,557,697 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e941cf01cee0204f9452282e9e315abab9623ab143c76529c1546597df5126b0
View on Chainz β†—

Height

#255,022

Difficulty

9.973726

Transactions

1

Size

208 B

Version

2

Bits

09f94623

Nonce

4,355

Timestamp

11/11/2013, 1:24:21 AM

Confirmations

6,557,697

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

d11a46c24c0fdebde24d37e6f747a83763d99f1c139e18691c1a981c45cfe504
Transactions (1)
Coinbased11a46c24c0fde…1a981c45cfe504
1 in β†’ 1 out10.0400 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.358 Γ— 10⁹⁹(100-digit number)
13587466991537278939…15567094646267831041
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
1.358 Γ— 10⁹⁹(100-digit number)
13587466991537278939…15567094646267831041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.717 Γ— 10⁹⁹(100-digit number)
27174933983074557879…31134189292535662081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.434 Γ— 10⁹⁹(100-digit number)
54349867966149115758…62268378585071324161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.086 Γ— 10¹⁰⁰(101-digit number)
10869973593229823151…24536757170142648321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.173 Γ— 10¹⁰⁰(101-digit number)
21739947186459646303…49073514340285296641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.347 Γ— 10¹⁰⁰(101-digit number)
43479894372919292606…98147028680570593281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.695 Γ— 10¹⁰⁰(101-digit number)
86959788745838585213…96294057361141186561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.739 Γ— 10¹⁰¹(102-digit number)
17391957749167717042…92588114722282373121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.478 Γ— 10¹⁰¹(102-digit number)
34783915498335434085…85176229444564746241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.956 Γ— 10¹⁰¹(102-digit number)
69567830996670868170…70352458889129492481
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:57,745,791 XPMΒ·at block #6,812,718 Β· updates every 60s
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