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Block #2,122,799

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/18/2017, 9:13:04 PM Β· Difficulty 10.9156 Β· 4,722,152 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1556603fac6a7c74e98c01cc02531fff9f2152352421407efae2685dc86c642e
View on Chainz β†—

Height

#2,122,799

Difficulty

10.915560

Transactions

1

Size

199 B

Version

2

Bits

0aea6226

Nonce

215,441,369

Timestamp

5/18/2017, 9:13:04 PM

Confirmations

4,722,152

Mined by

⛏️ P2SHATEaAFHgp4GbDp1STbyDe31zgU7y8ErACc

Merkle Root

8e18664106ef90fcd7a478dde64bde91fe501ee25739c41bc968a005e15d4ff4
Transactions (1)
Coinbase8e18664106ef90…68a005e15d4ff4
1 in β†’ 1 out8.3800 XPM109 B
ATEaAFHg…7y8ErACc
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.

1.227 Γ— 10⁹⁴(95-digit number)
12277538565508462639…57215596442127125621
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
1.227 Γ— 10⁹⁴(95-digit number)
12277538565508462639…57215596442127125621
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.455 Γ— 10⁹⁴(95-digit number)
24555077131016925279…14431192884254251241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.911 Γ— 10⁹⁴(95-digit number)
49110154262033850559…28862385768508502481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.822 Γ— 10⁹⁴(95-digit number)
98220308524067701118…57724771537017004961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.964 Γ— 10⁹⁡(96-digit number)
19644061704813540223…15449543074034009921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.928 Γ— 10⁹⁡(96-digit number)
39288123409627080447…30899086148068019841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.857 Γ— 10⁹⁡(96-digit number)
78576246819254160894…61798172296136039681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.571 Γ— 10⁹⁢(97-digit number)
15715249363850832178…23596344592272079361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.143 Γ— 10⁹⁢(97-digit number)
31430498727701664357…47192689184544158721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.286 Γ— 10⁹⁢(97-digit number)
62860997455403328715…94385378369088317441
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:58,004,025 XPMΒ·at block #6,844,950 Β· updates every 60s
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