Block #230,994

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/28/2013, 4:08:17 AM · Difficulty 9.9401 · 6,586,004 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
59400d7eb372f74186246cbcadbc38ec79e484304b87a2688f032aa3c9739104

Height

#230,994

Difficulty

9.940097

Transactions

7

Size

9.55 KB

Version

2

Bits

09f0aa2c

Nonce

92,867

Timestamp

10/28/2013, 4:08:17 AM

Confirmations

6,586,004

Merkle Root

905cd100d464e7e7541c3477997afefa0c96fe0699088b8781af233b7f597cb7
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.

6.071 × 10⁹¹(92-digit number)
60713555266516293179…16386388225055013379
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
6.071 × 10⁹¹(92-digit number)
60713555266516293179…16386388225055013379
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.214 × 10⁹²(93-digit number)
12142711053303258635…32772776450110026759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.428 × 10⁹²(93-digit number)
24285422106606517271…65545552900220053519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.857 × 10⁹²(93-digit number)
48570844213213034543…31091105800440107039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
9.714 × 10⁹²(93-digit number)
97141688426426069087…62182211600880214079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.942 × 10⁹³(94-digit number)
19428337685285213817…24364423201760428159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.885 × 10⁹³(94-digit number)
38856675370570427634…48728846403520856319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.771 × 10⁹³(94-digit number)
77713350741140855269…97457692807041712639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.554 × 10⁹⁴(95-digit number)
15542670148228171053…94915385614083425279
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,780,016 XPM·at block #6,816,997 · updates every 60s
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