Block #476,834

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 4/6/2014, 2:28:23 AM · Difficulty 10.4746 · 6,326,806 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7d98c9eff2464a8628cc9afe7f9fcfb19e19e4aaa91b428688bb326f528e9a59

Height

#476,834

Difficulty

10.474580

Transactions

1

Size

901 B

Version

2

Bits

0a797e0e

Nonce

14,377

Timestamp

4/6/2014, 2:28:23 AM

Confirmations

6,326,806

Merkle Root

740b86aa0bf67e5ff12b819b1a4507ed2b83b6407d66041aaa63d1c235ddf44d
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.

6.854 × 10⁹⁵(96-digit number)
68548910457363683615…81823416237731694079
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
6.854 × 10⁹⁵(96-digit number)
68548910457363683615…81823416237731694079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.370 × 10⁹⁶(97-digit number)
13709782091472736723…63646832475463388159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.741 × 10⁹⁶(97-digit number)
27419564182945473446…27293664950926776319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.483 × 10⁹⁶(97-digit number)
54839128365890946892…54587329901853552639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.096 × 10⁹⁷(98-digit number)
10967825673178189378…09174659803707105279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.193 × 10⁹⁷(98-digit number)
21935651346356378756…18349319607414210559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.387 × 10⁹⁷(98-digit number)
43871302692712757513…36698639214828421119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
8.774 × 10⁹⁷(98-digit number)
87742605385425515027…73397278429656842239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.754 × 10⁹⁸(99-digit number)
17548521077085103005…46794556859313684479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.509 × 10⁹⁸(99-digit number)
35097042154170206011…93589113718627368959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
7.019 × 10⁹⁸(99-digit number)
70194084308340412022…87178227437254737919
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,673,151 XPM·at block #6,803,639 · updates every 60s
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