Block #665,331

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.

2.429 × 10⁹⁷(98-digit number)

24291252995041777196…68255121644070297599

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

2.429 × 10⁹⁷(98-digit number)

24291252995041777196…68255121644070297599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.858 × 10⁹⁷(98-digit number)

48582505990083554392…36510243288140595199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

9.716 × 10⁹⁷(98-digit number)

97165011980167108785…73020486576281190399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.943 × 10⁹⁸(99-digit number)

19433002396033421757…46040973152562380799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.886 × 10⁹⁸(99-digit number)

38866004792066843514…92081946305124761599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.773 × 10⁹⁸(99-digit number)

77732009584133687028…84163892610249523199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.554 × 10⁹⁹(100-digit number)

15546401916826737405…68327785220499046399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.109 × 10⁹⁹(100-digit number)

31092803833653474811…36655570440998092799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.218 × 10⁹⁹(100-digit number)

62185607667306949622…73311140881996185599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.243 × 10¹⁰⁰(101-digit number)

12437121533461389924…46622281763992371199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

2.487 × 10¹⁰⁰(101-digit number)

24874243066922779849…93244563527984742399

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, …

Cross-reference on Chainz Explorer

Block #665,331

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