Block #1,422,505

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/21/2016, 12:27:53 PM · Difficulty 10.7802 · 5,395,530 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4c290af4b67293b772f7d7ac5c6b179734123dee3d320ba8e38ea01c14c915c0

Height

#1,422,505

Difficulty

10.780246

Transactions

3

Size

3.33 KB

Version

2

Bits

0ac7be35

Nonce

181,480,303

Timestamp

1/21/2016, 12:27:53 PM

Confirmations

5,395,530

Merkle Root

271a558fdc82ed6e4ceef30653158e538f70c4a85054a77ba717ce9a0294cf12
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

8.444 × 10⁹²(93-digit number)
84447966308516328761…11108635863636218799
Discovered Prime Numbers
p_k = 2^k × 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
8.444 × 10⁹²(93-digit number)
84447966308516328761…11108635863636218799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.688 × 10⁹³(94-digit number)
16889593261703265752…22217271727272437599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.377 × 10⁹³(94-digit number)
33779186523406531504…44434543454544875199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.755 × 10⁹³(94-digit number)
67558373046813063008…88869086909089750399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.351 × 10⁹⁴(95-digit number)
13511674609362612601…77738173818179500799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.702 × 10⁹⁴(95-digit number)
27023349218725225203…55476347636359001599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.404 × 10⁹⁴(95-digit number)
54046698437450450407…10952695272718003199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.080 × 10⁹⁵(96-digit number)
10809339687490090081…21905390545436006399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.161 × 10⁹⁵(96-digit number)
21618679374980180162…43810781090872012799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.323 × 10⁹⁵(96-digit number)
43237358749960360325…87621562181744025599
Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆
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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)
Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,788,349 XPM·at block #6,818,034 · updates every 60s
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