Block #409,632

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.

3.343 × 10⁹⁸(99-digit number)

33433306386958985660…77560836232487852499

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

3.343 × 10⁹⁸(99-digit number)

33433306386958985660…77560836232487852499

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.686 × 10⁹⁸(99-digit number)

66866612773917971321…55121672464975704999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.337 × 10⁹⁹(100-digit number)

13373322554783594264…10243344929951409999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.674 × 10⁹⁹(100-digit number)

26746645109567188528…20486689859902819999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.349 × 10⁹⁹(100-digit number)

53493290219134377057…40973379719805639999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.069 × 10¹⁰⁰(101-digit number)

10698658043826875411…81946759439611279999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.139 × 10¹⁰⁰(101-digit number)

21397316087653750822…63893518879222559999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.279 × 10¹⁰⁰(101-digit number)

42794632175307501645…27787037758445119999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

8.558 × 10¹⁰⁰(101-digit number)

85589264350615003291…55574075516890239999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.711 × 10¹⁰¹(102-digit number)

17117852870123000658…11148151033780479999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

3.423 × 10¹⁰¹(102-digit number)

34235705740246001316…22296302067560959999

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 #409,632

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