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Block #2,224,755

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/27/2017, 4:49:54 AM Β· Difficulty 10.9472 Β· 4,605,741 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b2b8870c34d52d7a13cd91a0ed3caa3f582f4464dee7a919dd7a177aa827447f
View on Chainz β†—

Height

#2,224,755

Difficulty

10.947160

Transactions

2

Size

1020 B

Version

2

Bits

0af2790f

Nonce

1,460,769,456

Timestamp

7/27/2017, 4:49:54 AM

Confirmations

4,605,741

Mined by

⛏️ P2SHAbrSQ1CapWdX275NyqZ48XKb8FT2dpQara

Merkle Root

31091484833df92467f8f92a4c757d857ee998017ee499ad75979236c49e148e
Transactions (2)
Coinbasee3ee38d16487b9…10042a77d5402e
1 in β†’ 1 out8.3400 XPM110 B
AbrSQ1Ca…T2dpQara
fabf224ea8d338…ea0f11b1680fa6
5 in β†’ 2 out802.3589 XPM819 B
AekbApso…2AQHu3maAdLv38Pf…k1z3e6Dc
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.

5.131 Γ— 10⁹⁢(97-digit number)
51319580066535930920…16585234464915425281
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
5.131 Γ— 10⁹⁢(97-digit number)
51319580066535930920…16585234464915425281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.026 Γ— 10⁹⁷(98-digit number)
10263916013307186184…33170468929830850561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.052 Γ— 10⁹⁷(98-digit number)
20527832026614372368…66340937859661701121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.105 Γ— 10⁹⁷(98-digit number)
41055664053228744736…32681875719323402241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.211 Γ— 10⁹⁷(98-digit number)
82111328106457489472…65363751438646804481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.642 Γ— 10⁹⁸(99-digit number)
16422265621291497894…30727502877293608961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.284 Γ— 10⁹⁸(99-digit number)
32844531242582995789…61455005754587217921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.568 Γ— 10⁹⁸(99-digit number)
65689062485165991578…22910011509174435841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.313 Γ— 10⁹⁹(100-digit number)
13137812497033198315…45820023018348871681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.627 Γ— 10⁹⁹(100-digit number)
26275624994066396631…91640046036697743361
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:57,888,216 XPMΒ·at block #6,830,495 Β· updates every 60s
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