Block #480,614

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 4/8/2014, 10:12:20 AM · Difficulty 10.5189 · 6,327,320 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e17e4cc8589291e7742e7b299355e230a44209814372fae149861ddcffe861f0

Height

#480,614

Difficulty

10.518903

Transactions

1

Size

936 B

Version

2

Bits

0a84d6db

Nonce

182,231

Timestamp

4/8/2014, 10:12:20 AM

Confirmations

6,327,320

Merkle Root

8da54a5975b76ed2918683817126faab94fb3f126630dbfd091d42a90e484868
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.

1.300 × 10⁹⁶(97-digit number)
13007640899027558748…58834975252559639379
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
1.300 × 10⁹⁶(97-digit number)
13007640899027558748…58834975252559639379
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.601 × 10⁹⁶(97-digit number)
26015281798055117497…17669950505119278759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.203 × 10⁹⁶(97-digit number)
52030563596110234995…35339901010238557519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.040 × 10⁹⁷(98-digit number)
10406112719222046999…70679802020477115039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.081 × 10⁹⁷(98-digit number)
20812225438444093998…41359604040954230079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.162 × 10⁹⁷(98-digit number)
41624450876888187996…82719208081908460159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
8.324 × 10⁹⁷(98-digit number)
83248901753776375992…65438416163816920319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.664 × 10⁹⁸(99-digit number)
16649780350755275198…30876832327633840639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.329 × 10⁹⁸(99-digit number)
33299560701510550396…61753664655267681279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
6.659 × 10⁹⁸(99-digit number)
66599121403021100793…23507329310535362559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.331 × 10⁹⁹(100-digit number)
13319824280604220158…47014658621070725119
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:57,707,510 XPM·at block #6,807,933 · updates every 60s
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