Block #483,596

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/10/2014, 3:31:57 AM · Difficulty 10.5659 · 6,321,494 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
47781466c23cd026e10aa8243f0749101ddc2aa9b0b47ee2de30f5940daec52d

Height

#483,596

Difficulty

10.565917

Transactions

1

Size

903 B

Version

2

Bits

0a90dff6

Nonce

9,851

Timestamp

4/10/2014, 3:31:57 AM

Confirmations

6,321,494

Merkle Root

ef16b4104d92f88a9c4eae6da95f2bad31e63064dae5bddd162cccfbed353bb9
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.

8.527 × 10⁹⁸(99-digit number)
85276119666629482940…98357853554514431999
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
8.527 × 10⁹⁸(99-digit number)
85276119666629482940…98357853554514431999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.705 × 10⁹⁹(100-digit number)
17055223933325896588…96715707109028863999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.411 × 10⁹⁹(100-digit number)
34110447866651793176…93431414218057727999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.822 × 10⁹⁹(100-digit number)
68220895733303586352…86862828436115455999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.364 × 10¹⁰⁰(101-digit number)
13644179146660717270…73725656872230911999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.728 × 10¹⁰⁰(101-digit number)
27288358293321434541…47451313744461823999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.457 × 10¹⁰⁰(101-digit number)
54576716586642869082…94902627488923647999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.091 × 10¹⁰¹(102-digit number)
10915343317328573816…89805254977847295999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.183 × 10¹⁰¹(102-digit number)
21830686634657147632…79610509955694591999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.366 × 10¹⁰¹(102-digit number)
43661373269314295265…59221019911389183999
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:57,684,785 XPM·at block #6,805,089 · updates every 60s
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