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Block #2,111,590

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/11/2017, 1:52:49 PM Β· Difficulty 10.9028 Β· 4,731,531 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ae2366c7181b36317ec673676c68c72a9e75e3dfbccd875d5a034761f83b5acb
View on Chainz β†—

Height

#2,111,590

Difficulty

10.902826

Transactions

1

Size

198 B

Version

2

Bits

0ae71f97

Nonce

1,493,881,411

Timestamp

5/11/2017, 1:52:49 PM

Confirmations

4,731,531

Mined by

⛏️ P2SHAGKCNaA72w8NgdHcGYL7Z93hLxeiZjRkak

Merkle Root

d551130c7efef88bf5c5843a4aab63b7ea2b7df12e5ec314ca3e5c8718b3e70e
Transactions (1)
Coinbased551130c7efef8…3e5c8718b3e70e
1 in β†’ 1 out8.4000 XPM109 B
AGKCNaA7…eiZjRkak
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.

1.162 Γ— 10⁹³(94-digit number)
11620649896071764258…46628679132685038401
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
1.162 Γ— 10⁹³(94-digit number)
11620649896071764258…46628679132685038401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.324 Γ— 10⁹³(94-digit number)
23241299792143528517…93257358265370076801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.648 Γ— 10⁹³(94-digit number)
46482599584287057034…86514716530740153601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.296 Γ— 10⁹³(94-digit number)
92965199168574114068…73029433061480307201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.859 Γ— 10⁹⁴(95-digit number)
18593039833714822813…46058866122960614401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.718 Γ— 10⁹⁴(95-digit number)
37186079667429645627…92117732245921228801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.437 Γ— 10⁹⁴(95-digit number)
74372159334859291255…84235464491842457601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.487 Γ— 10⁹⁡(96-digit number)
14874431866971858251…68470928983684915201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.974 Γ— 10⁹⁡(96-digit number)
29748863733943716502…36941857967369830401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.949 Γ— 10⁹⁡(96-digit number)
59497727467887433004…73883715934739660801
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:57,989,333 XPMΒ·at block #6,843,120 Β· updates every 60s
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