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Block #1,698,214

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/1/2016, 12:20:03 PM Β· Difficulty 10.6719 Β· 5,143,935 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
82acf148ff3256a747b17ba59ce9f4e71be3d2d656b9e676c232e3c0e3fa2542
View on Chainz β†—

Height

#1,698,214

Difficulty

10.671938

Transactions

1

Size

200 B

Version

2

Bits

0aac041c

Nonce

266,138,861

Timestamp

8/1/2016, 12:20:03 PM

Confirmations

5,143,935

Mined by

⛏️ P2SHAZNb3PShKatQzMkDvRVKE4aWiPViMEnEwc

Merkle Root

9e63c5bbea2e12cc9b66025ccd076e4250528e01889f288e1ee87b47110e5ed9
Transactions (1)
Coinbase9e63c5bbea2e12…e87b47110e5ed9
1 in β†’ 1 out8.7700 XPM109 B
AZNb3PSh…ViMEnEwc
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.

4.777 Γ— 10⁹⁢(97-digit number)
47778514727653758217…73826630215329863679
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
4.777 Γ— 10⁹⁢(97-digit number)
47778514727653758217…73826630215329863679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.555 Γ— 10⁹⁢(97-digit number)
95557029455307516435…47653260430659727359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.911 Γ— 10⁹⁷(98-digit number)
19111405891061503287…95306520861319454719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.822 Γ— 10⁹⁷(98-digit number)
38222811782123006574…90613041722638909439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.644 Γ— 10⁹⁷(98-digit number)
76445623564246013148…81226083445277818879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.528 Γ— 10⁹⁸(99-digit number)
15289124712849202629…62452166890555637759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.057 Γ— 10⁹⁸(99-digit number)
30578249425698405259…24904333781111275519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.115 Γ— 10⁹⁸(99-digit number)
61156498851396810518…49808667562222551039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.223 Γ— 10⁹⁹(100-digit number)
12231299770279362103…99617335124445102079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.446 Γ— 10⁹⁹(100-digit number)
24462599540558724207…99234670248890204159
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,981,581 XPMΒ·at block #6,842,148 Β· updates every 60s
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