Block #343,023

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.

1.227 × 10⁹⁷(98-digit number)

12274139154421548114…98019800102761121279

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

1.227 × 10⁹⁷(98-digit number)

12274139154421548114…98019800102761121279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.454 × 10⁹⁷(98-digit number)

24548278308843096228…96039600205522242559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.909 × 10⁹⁷(98-digit number)

49096556617686192456…92079200411044485119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.819 × 10⁹⁷(98-digit number)

98193113235372384913…84158400822088970239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.963 × 10⁹⁸(99-digit number)

19638622647074476982…68316801644177940479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.927 × 10⁹⁸(99-digit number)

39277245294148953965…36633603288355880959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.855 × 10⁹⁸(99-digit number)

78554490588297907930…73267206576711761919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.571 × 10⁹⁹(100-digit number)

15710898117659581586…46534413153423523839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.142 × 10⁹⁹(100-digit number)

31421796235319163172…93068826306847047679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

6.284 × 10⁹⁹(100-digit number)

62843592470638326344…86137652613694095359

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