Block #473,228

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/3/2014, 6:17:03 PM · Difficulty 10.4474 · 6,330,279 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
732a028e8beb219fb9c136b9a8815fa3d2babdc8ee13e0da59375567ae9ef6ff

Height

#473,228

Difficulty

10.447351

Transactions

5

Size

2.32 KB

Version

2

Bits

0a7285a0

Nonce

107,542

Timestamp

4/3/2014, 6:17:03 PM

Confirmations

6,330,279

Merkle Root

ff58dd8ceadde6ccda8d9d9c21f11e2b90107dc901334784ca4780e263b33a19
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.

1.311 × 10¹⁰⁴(105-digit number)
13119294871702317300…10500292867533183999
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
1.311 × 10¹⁰⁴(105-digit number)
13119294871702317300…10500292867533183999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.623 × 10¹⁰⁴(105-digit number)
26238589743404634600…21000585735066367999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.247 × 10¹⁰⁴(105-digit number)
52477179486809269201…42001171470132735999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.049 × 10¹⁰⁵(106-digit number)
10495435897361853840…84002342940265471999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.099 × 10¹⁰⁵(106-digit number)
20990871794723707680…68004685880530943999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.198 × 10¹⁰⁵(106-digit number)
41981743589447415360…36009371761061887999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
8.396 × 10¹⁰⁵(106-digit number)
83963487178894830721…72018743522123775999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.679 × 10¹⁰⁶(107-digit number)
16792697435778966144…44037487044247551999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.358 × 10¹⁰⁶(107-digit number)
33585394871557932288…88074974088495103999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
6.717 × 10¹⁰⁶(107-digit number)
67170789743115864577…76149948176990207999
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:57,672,080 XPM·at block #6,803,506 · updates every 60s
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