Block #495,642

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.

2.280 × 10⁹⁸(99-digit number)

22803143972627859440…90523322088403735039

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

2.280 × 10⁹⁸(99-digit number)

22803143972627859440…90523322088403735039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.560 × 10⁹⁸(99-digit number)

45606287945255718880…81046644176807470079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

9.121 × 10⁹⁸(99-digit number)

91212575890511437760…62093288353614940159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.824 × 10⁹⁹(100-digit number)

18242515178102287552…24186576707229880319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.648 × 10⁹⁹(100-digit number)

36485030356204575104…48373153414459760639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.297 × 10⁹⁹(100-digit number)

72970060712409150208…96746306828919521279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.459 × 10¹⁰⁰(101-digit number)

14594012142481830041…93492613657839042559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.918 × 10¹⁰⁰(101-digit number)

29188024284963660083…86985227315678085119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.837 × 10¹⁰⁰(101-digit number)

58376048569927320166…73970454631356170239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.167 × 10¹⁰¹(102-digit number)

11675209713985464033…47940909262712340479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

2.335 × 10¹⁰¹(102-digit number)

23350419427970928066…95881818525424680959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^11 × origin − 1

4.670 × 10¹⁰¹(102-digit number)

46700838855941856133…91763637050849361919

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 #495,642

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