Block #2,282,933

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.

2.773 × 10⁹⁶(97-digit number)

27730572068432582585…65244923095171020799

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

2.773 × 10⁹⁶(97-digit number)

27730572068432582585…65244923095171020799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.546 × 10⁹⁶(97-digit number)

55461144136865165171…30489846190342041599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.109 × 10⁹⁷(98-digit number)

11092228827373033034…60979692380684083199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.218 × 10⁹⁷(98-digit number)

22184457654746066068…21959384761368166399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.436 × 10⁹⁷(98-digit number)

44368915309492132137…43918769522736332799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.873 × 10⁹⁷(98-digit number)

88737830618984264274…87837539045472665599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.774 × 10⁹⁸(99-digit number)

17747566123796852854…75675078090945331199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.549 × 10⁹⁸(99-digit number)

35495132247593705709…51350156181890662399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.099 × 10⁹⁸(99-digit number)

70990264495187411419…02700312363781324799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.419 × 10⁹⁹(100-digit number)

14198052899037482283…05400624727562649599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

2.839 × 10⁹⁹(100-digit number)

28396105798074964567…10801249455125299199

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 #2,282,933

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