Block #663,313

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.

3.820 × 10⁹⁷(98-digit number)

38205613029446820846…35048523694501754879

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

3.820 × 10⁹⁷(98-digit number)

38205613029446820846…35048523694501754879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.641 × 10⁹⁷(98-digit number)

76411226058893641692…70097047389003509759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.528 × 10⁹⁸(99-digit number)

15282245211778728338…40194094778007019519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.056 × 10⁹⁸(99-digit number)

30564490423557456677…80388189556014039039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.112 × 10⁹⁸(99-digit number)

61128980847114913354…60776379112028078079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.222 × 10⁹⁹(100-digit number)

12225796169422982670…21552758224056156159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.445 × 10⁹⁹(100-digit number)

24451592338845965341…43105516448112312319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.890 × 10⁹⁹(100-digit number)

48903184677691930683…86211032896224624639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.780 × 10⁹⁹(100-digit number)

97806369355383861366…72422065792449249279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.956 × 10¹⁰⁰(101-digit number)

19561273871076772273…44844131584898498559

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