Block #366,359

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/19/2014, 8:55:21 AM · Difficulty 10.4293 · 6,434,650 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

aae38715c21833c4e6aa38bbdf22566e286d6ceb9fe90aa1614acda2845d385e

View on Chainz ↗

Height

#366,359

Difficulty

10.429329

Transactions

Size

903 B

Version

Bits

0a6de884

Nonce

145,976

Timestamp

1/19/2014, 8:55:21 AM

Confirmations

6,434,650

Mined by

⛏️ aRNAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

7864ee5d460bb6a8b068b129bc677c46d7a061d7ab0971066a488f17e6feb18b

Transactions (1)

Coinbase7864ee5d460bb6…488f17e6feb18b

1 in → 22 out9.1800 XPM811 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AZV4TwxQ…8JnQqSoH Ad9pSzHt…cpJ3y2zz

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.

1.450 × 10⁹⁹(100-digit number)

14501348898489068262…07643180734793607039

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.

origin − 1

1.450 × 10⁹⁹(100-digit number)

14501348898489068262…07643180734793607039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.900 × 10⁹⁹(100-digit number)

29002697796978136525…15286361469587214079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.800 × 10⁹⁹(100-digit number)

58005395593956273050…30572722939174428159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.160 × 10¹⁰⁰(101-digit number)

11601079118791254610…61145445878348856319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.320 × 10¹⁰⁰(101-digit number)

23202158237582509220…22290891756697712639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.640 × 10¹⁰⁰(101-digit number)

46404316475165018440…44581783513395425279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

9.280 × 10¹⁰⁰(101-digit number)

92808632950330036880…89163567026790850559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.856 × 10¹⁰¹(102-digit number)

18561726590066007376…78327134053581701119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.712 × 10¹⁰¹(102-digit number)

37123453180132014752…56654268107163402239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

7.424 × 10¹⁰¹(102-digit number)

74246906360264029504…13308536214326804479

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, …

Cross-reference on Chainz Explorer