Block #563,632

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.

2.196 × 10⁹⁷(98-digit number)

21963714608391842579…46926041790699329559

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

2.196 × 10⁹⁷(98-digit number)

21963714608391842579…46926041790699329559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.392 × 10⁹⁷(98-digit number)

43927429216783685158…93852083581398659119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

8.785 × 10⁹⁷(98-digit number)

87854858433567370316…87704167162797318239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.757 × 10⁹⁸(99-digit number)

17570971686713474063…75408334325594636479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.514 × 10⁹⁸(99-digit number)

35141943373426948126…50816668651189272959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.028 × 10⁹⁸(99-digit number)

70283886746853896253…01633337302378545919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.405 × 10⁹⁹(100-digit number)

14056777349370779250…03266674604757091839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.811 × 10⁹⁹(100-digit number)

28113554698741558501…06533349209514183679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.622 × 10⁹⁹(100-digit number)

56227109397483117002…13066698419028367359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.124 × 10¹⁰⁰(101-digit number)

11245421879496623400…26133396838056734719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

2.249 × 10¹⁰⁰(101-digit number)

22490843758993246801…52266793676113469439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^11 × origin − 1

4.498 × 10¹⁰⁰(101-digit number)

44981687517986493602…04533587352226938879

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 #563,632

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