Block #2,784,801

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.

2.438 × 10⁹³(94-digit number)

24383020750999558242…42055579570073203921

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

2.438 × 10⁹³(94-digit number)

24383020750999558242…42055579570073203921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.876 × 10⁹³(94-digit number)

48766041501999116485…84111159140146407841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.753 × 10⁹³(94-digit number)

97532083003998232970…68222318280292815681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.950 × 10⁹⁴(95-digit number)

19506416600799646594…36444636560585631361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.901 × 10⁹⁴(95-digit number)

39012833201599293188…72889273121171262721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.802 × 10⁹⁴(95-digit number)

78025666403198586376…45778546242342525441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.560 × 10⁹⁵(96-digit number)

15605133280639717275…91557092484685050881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.121 × 10⁹⁵(96-digit number)

31210266561279434550…83114184969370101761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.242 × 10⁹⁵(96-digit number)

62420533122558869101…66228369938740203521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.248 × 10⁹⁶(97-digit number)

12484106624511773820…32456739877480407041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

2.496 × 10⁹⁶(97-digit number)

24968213249023547640…64913479754960814081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^11 × origin + 1

4.993 × 10⁹⁶(97-digit number)

49936426498047095281…29826959509921628161

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 #2,784,801

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