Block #433,026

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/7/2014, 7:52:25 AM · Difficulty 10.3405 · 6,372,533 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

bbd79290e26da253eca57ed72ea2c7dcad9661c650e399b81fc8e783602fe904

View on Chainz ↗

Height

#433,026

Difficulty

10.340526

Transactions

Size

903 B

Version

Bits

0a572cbd

Nonce

97,762

Timestamp

3/7/2014, 7:52:25 AM

Confirmations

6,372,533

Mined by

⛏️ aSz?AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

667c07a3beafb479e0b2954278ae505fec6edc67d1480ff7ec7bd81868456470

Transactions (1)

Coinbase667c07a3beafb4…7bd81868456470

1 in → 22 out9.3400 XPM811 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

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.

1.397 × 10¹⁰⁰(101-digit number)

13971823816121051680…81727116298331735199

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

1.397 × 10¹⁰⁰(101-digit number)

13971823816121051680…81727116298331735199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.794 × 10¹⁰⁰(101-digit number)

27943647632242103360…63454232596663470399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.588 × 10¹⁰⁰(101-digit number)

55887295264484206720…26908465193326940799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.117 × 10¹⁰¹(102-digit number)

11177459052896841344…53816930386653881599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.235 × 10¹⁰¹(102-digit number)

22354918105793682688…07633860773307763199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.470 × 10¹⁰¹(102-digit number)

44709836211587365376…15267721546615526399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

8.941 × 10¹⁰¹(102-digit number)

89419672423174730752…30535443093231052799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.788 × 10¹⁰²(103-digit number)

17883934484634946150…61070886186462105599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.576 × 10¹⁰²(103-digit number)

35767868969269892301…22141772372924211199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

7.153 × 10¹⁰²(103-digit number)

71535737938539784602…44283544745848422399

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