Block #497,180

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.

8.681 × 10⁹⁸(99-digit number)

86814852998119687219…95413002033180145601

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

8.681 × 10⁹⁸(99-digit number)

86814852998119687219…95413002033180145601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.736 × 10⁹⁹(100-digit number)

17362970599623937443…90826004066360291201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.472 × 10⁹⁹(100-digit number)

34725941199247874887…81652008132720582401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

6.945 × 10⁹⁹(100-digit number)

69451882398495749775…63304016265441164801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.389 × 10¹⁰⁰(101-digit number)

13890376479699149955…26608032530882329601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.778 × 10¹⁰⁰(101-digit number)

27780752959398299910…53216065061764659201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.556 × 10¹⁰⁰(101-digit number)

55561505918796599820…06432130123529318401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.111 × 10¹⁰¹(102-digit number)

11112301183759319964…12864260247058636801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.222 × 10¹⁰¹(102-digit number)

22224602367518639928…25728520494117273601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

4.444 × 10¹⁰¹(102-digit number)

44449204735037279856…51457040988234547201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

8.889 × 10¹⁰¹(102-digit number)

88898409470074559712…02914081976469094401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^11 × origin + 1

1.777 × 10¹⁰²(103-digit number)

17779681894014911942…05828163952938188801

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 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

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 2CC formula:

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

Cross-reference on Chainz Explorer