Block #839,712

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.

8.525 × 10⁹⁵(96-digit number)

85257643292319522682…26007740493183864319

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

8.525 × 10⁹⁵(96-digit number)

85257643292319522682…26007740493183864319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.705 × 10⁹⁶(97-digit number)

17051528658463904536…52015480986367728639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.410 × 10⁹⁶(97-digit number)

34103057316927809072…04030961972735457279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.820 × 10⁹⁶(97-digit number)

68206114633855618145…08061923945470914559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.364 × 10⁹⁷(98-digit number)

13641222926771123629…16123847890941829119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.728 × 10⁹⁷(98-digit number)

27282445853542247258…32247695781883658239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.456 × 10⁹⁷(98-digit number)

54564891707084494516…64495391563767316479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.091 × 10⁹⁸(99-digit number)

10912978341416898903…28990783127534632959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.182 × 10⁹⁸(99-digit number)

21825956682833797806…57981566255069265919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.365 × 10⁹⁸(99-digit number)

43651913365667595613…15963132510138531839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

8.730 × 10⁹⁸(99-digit number)

87303826731335191226…31926265020277063679

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 #839,712

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