Block #638,527

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.

1.920 × 10⁹⁸(99-digit number)

19202312744595137200…13337182607020195841

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

1.920 × 10⁹⁸(99-digit number)

19202312744595137200…13337182607020195841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.840 × 10⁹⁸(99-digit number)

38404625489190274400…26674365214040391681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

7.680 × 10⁹⁸(99-digit number)

76809250978380548800…53348730428080783361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.536 × 10⁹⁹(100-digit number)

15361850195676109760…06697460856161566721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.072 × 10⁹⁹(100-digit number)

30723700391352219520…13394921712323133441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

6.144 × 10⁹⁹(100-digit number)

61447400782704439040…26789843424646266881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.228 × 10¹⁰⁰(101-digit number)

12289480156540887808…53579686849292533761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.457 × 10¹⁰⁰(101-digit number)

24578960313081775616…07159373698585067521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.915 × 10¹⁰⁰(101-digit number)

49157920626163551232…14318747397170135041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

9.831 × 10¹⁰⁰(101-digit number)

98315841252327102465…28637494794340270081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

1.966 × 10¹⁰¹(102-digit number)

19663168250465420493…57274989588680540161

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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer

Block #638,527

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