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Block #1,808,121

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/14/2016, 1:03:46 PM Β· Difficulty 10.8321 Β· 5,019,025 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0d895fdd765e5615d8a6a00f36b16ed267e7468e08e4dfb8ed4eca0ac61617eb
View on Chainz β†—

Height

#1,808,121

Difficulty

10.832122

Transactions

1

Size

200 B

Version

2

Bits

0ad505f4

Nonce

1,889,086,482

Timestamp

10/14/2016, 1:03:46 PM

Confirmations

5,019,025

Mined by

⛏️ P2SHAP68jyL7SCBvpn9qc3dxJWMPQ3VXt79DP9

Merkle Root

94241b89815b27283ab3211f58a22881c916a2d5ec3057d44417cebbcff4a3dd
Transactions (1)
Coinbase94241b89815b27…17cebbcff4a3dd
1 in β†’ 1 out8.5100 XPM110 B
AP68jyL7…VXt79DP9
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.

3.352 Γ— 10⁹⁡(96-digit number)
33528806625053558769…95090601743478652001
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
3.352 Γ— 10⁹⁡(96-digit number)
33528806625053558769…95090601743478652001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.705 Γ— 10⁹⁡(96-digit number)
67057613250107117538…90181203486957304001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.341 Γ— 10⁹⁢(97-digit number)
13411522650021423507…80362406973914608001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.682 Γ— 10⁹⁢(97-digit number)
26823045300042847015…60724813947829216001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.364 Γ— 10⁹⁢(97-digit number)
53646090600085694031…21449627895658432001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.072 Γ— 10⁹⁷(98-digit number)
10729218120017138806…42899255791316864001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.145 Γ— 10⁹⁷(98-digit number)
21458436240034277612…85798511582633728001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.291 Γ— 10⁹⁷(98-digit number)
42916872480068555224…71597023165267456001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.583 Γ— 10⁹⁷(98-digit number)
85833744960137110449…43194046330534912001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.716 Γ— 10⁹⁸(99-digit number)
17166748992027422089…86388092661069824001
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:57,861,351 XPMΒ·at block #6,827,145 Β· updates every 60s
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