Block #1,336,397

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/22/2015, 3:08:48 AM · Difficulty 10.8112 · 5,462,777 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e87b9ce23a48a8c060d56c5afb4c87f3795125ae3866a02b5b2c107ae829a278

Height

#1,336,397

Difficulty

10.811202

Transactions

2

Size

6.19 KB

Version

2

Bits

0acfaaea

Nonce

293,094,873

Timestamp

11/22/2015, 3:08:48 AM

Confirmations

5,462,777

Merkle Root

fb39af6573ee2cb7bb723b0a9bb20a7febd21f8e5dd45396c6b2568e12cd5740
Transactions (2)
1 in → 1 out8.8000 XPM109 B
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.

2.260 × 10⁹²(93-digit number)
22602618607465224150…90194913981714299519
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
2.260 × 10⁹²(93-digit number)
22602618607465224150…90194913981714299519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.520 × 10⁹²(93-digit number)
45205237214930448300…80389827963428599039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
9.041 × 10⁹²(93-digit number)
90410474429860896601…60779655926857198079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.808 × 10⁹³(94-digit number)
18082094885972179320…21559311853714396159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.616 × 10⁹³(94-digit number)
36164189771944358640…43118623707428792319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.232 × 10⁹³(94-digit number)
72328379543888717281…86237247414857584639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.446 × 10⁹⁴(95-digit number)
14465675908777743456…72474494829715169279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.893 × 10⁹⁴(95-digit number)
28931351817555486912…44948989659430338559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.786 × 10⁹⁴(95-digit number)
57862703635110973825…89897979318860677119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.157 × 10⁹⁵(96-digit number)
11572540727022194765…79795958637721354239
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:57,637,428 XPM·at block #6,799,173 · updates every 60s
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