Block #1,183,397

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.

3.232 × 10⁹⁴(95-digit number)

32321219342018649483…72215661795137064961

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

3.232 × 10⁹⁴(95-digit number)

32321219342018649483…72215661795137064961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.464 × 10⁹⁴(95-digit number)

64642438684037298967…44431323590274129921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.292 × 10⁹⁵(96-digit number)

12928487736807459793…88862647180548259841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.585 × 10⁹⁵(96-digit number)

25856975473614919587…77725294361096519681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.171 × 10⁹⁵(96-digit number)

51713950947229839174…55450588722193039361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.034 × 10⁹⁶(97-digit number)

10342790189445967834…10901177444386078721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.068 × 10⁹⁶(97-digit number)

20685580378891935669…21802354888772157441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.137 × 10⁹⁶(97-digit number)

41371160757783871339…43604709777544314881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

8.274 × 10⁹⁶(97-digit number)

82742321515567742678…87209419555088629761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.654 × 10⁹⁷(98-digit number)

16548464303113548535…74418839110177259521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

3.309 × 10⁹⁷(98-digit number)

33096928606227097071…48837678220354519041

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 #1,183,397

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