Block #2,828,005

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.

1.319 × 10⁹⁴(95-digit number)

13193859588697317370…36806087392824941679

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

1.319 × 10⁹⁴(95-digit number)

13193859588697317370…36806087392824941679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.638 × 10⁹⁴(95-digit number)

26387719177394634741…73612174785649883359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.277 × 10⁹⁴(95-digit number)

52775438354789269483…47224349571299766719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.055 × 10⁹⁵(96-digit number)

10555087670957853896…94448699142599533439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.111 × 10⁹⁵(96-digit number)

21110175341915707793…88897398285199066879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.222 × 10⁹⁵(96-digit number)

42220350683831415586…77794796570398133759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

8.444 × 10⁹⁵(96-digit number)

84440701367662831173…55589593140796267519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.688 × 10⁹⁶(97-digit number)

16888140273532566234…11179186281592535039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.377 × 10⁹⁶(97-digit number)

33776280547065132469…22358372563185070079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

6.755 × 10⁹⁶(97-digit number)

67552561094130264938…44716745126370140159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

1.351 × 10⁹⁷(98-digit number)

13510512218826052987…89433490252740280319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^11 × origin − 1

2.702 × 10⁹⁷(98-digit number)

27021024437652105975…78866980505480560639

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 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

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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer

Block #2,828,005

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