Block #3,068,133

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.

3.801 × 10⁹⁴(95-digit number)

38017449840709873883…52418186054324698081

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

3.801 × 10⁹⁴(95-digit number)

38017449840709873883…52418186054324698081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

7.603 × 10⁹⁴(95-digit number)

76034899681419747766…04836372108649396161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.520 × 10⁹⁵(96-digit number)

15206979936283949553…09672744217298792321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.041 × 10⁹⁵(96-digit number)

30413959872567899106…19345488434597584641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

6.082 × 10⁹⁵(96-digit number)

60827919745135798212…38690976869195169281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.216 × 10⁹⁶(97-digit number)

12165583949027159642…77381953738390338561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.433 × 10⁹⁶(97-digit number)

24331167898054319285…54763907476780677121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.866 × 10⁹⁶(97-digit number)

48662335796108638570…09527814953561354241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

9.732 × 10⁹⁶(97-digit number)

97324671592217277140…19055629907122708481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.946 × 10⁹⁷(98-digit number)

19464934318443455428…38111259814245416961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

3.892 × 10⁹⁷(98-digit number)

38929868636886910856…76222519628490833921

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 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

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 2CC formula:

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

Cross-reference on Chainz Explorer

Block #3,068,133

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