Block #3,004,617

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.

3.981 × 10⁹³(94-digit number)

39815297474950476648…03393835203916660139

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

3.981 × 10⁹³(94-digit number)

39815297474950476648…03393835203916660139

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.963 × 10⁹³(94-digit number)

79630594949900953297…06787670407833320279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.592 × 10⁹⁴(95-digit number)

15926118989980190659…13575340815666640559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.185 × 10⁹⁴(95-digit number)

31852237979960381318…27150681631333281119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.370 × 10⁹⁴(95-digit number)

63704475959920762637…54301363262666562239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.274 × 10⁹⁵(96-digit number)

12740895191984152527…08602726525333124479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.548 × 10⁹⁵(96-digit number)

25481790383968305055…17205453050666248959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.096 × 10⁹⁵(96-digit number)

50963580767936610110…34410906101332497919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.019 × 10⁹⁶(97-digit number)

10192716153587322022…68821812202664995839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.038 × 10⁹⁶(97-digit number)

20385432307174644044…37643624405329991679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

4.077 × 10⁹⁶(97-digit number)

40770864614349288088…75287248810659983359

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 #3,004,617

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