Block #2,809,135

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.

9.714 × 10⁹⁴(95-digit number)

97141161417482359464…33967500424228265399

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

9.714 × 10⁹⁴(95-digit number)

97141161417482359464…33967500424228265399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.942 × 10⁹⁵(96-digit number)

19428232283496471892…67935000848456530799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.885 × 10⁹⁵(96-digit number)

38856464566992943785…35870001696913061599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.771 × 10⁹⁵(96-digit number)

77712929133985887571…71740003393826123199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.554 × 10⁹⁶(97-digit number)

15542585826797177514…43480006787652246399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.108 × 10⁹⁶(97-digit number)

31085171653594355028…86960013575304492799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.217 × 10⁹⁶(97-digit number)

62170343307188710057…73920027150608985599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.243 × 10⁹⁷(98-digit number)

12434068661437742011…47840054301217971199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.486 × 10⁹⁷(98-digit number)

24868137322875484022…95680108602435942399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.973 × 10⁹⁷(98-digit number)

49736274645750968045…91360217204871884799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

9.947 × 10⁹⁷(98-digit number)

99472549291501936091…82720434409743769599

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 #2,809,135

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