Block #3,007,742

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.

1.733 × 10⁹⁴(95-digit number)

17330438506882764890…21813812956024450039

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

1.733 × 10⁹⁴(95-digit number)

17330438506882764890…21813812956024450039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.466 × 10⁹⁴(95-digit number)

34660877013765529780…43627625912048900079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.932 × 10⁹⁴(95-digit number)

69321754027531059561…87255251824097800159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.386 × 10⁹⁵(96-digit number)

13864350805506211912…74510503648195600319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.772 × 10⁹⁵(96-digit number)

27728701611012423824…49021007296391200639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.545 × 10⁹⁵(96-digit number)

55457403222024847649…98042014592782401279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.109 × 10⁹⁶(97-digit number)

11091480644404969529…96084029185564802559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.218 × 10⁹⁶(97-digit number)

22182961288809939059…92168058371129605119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.436 × 10⁹⁶(97-digit number)

44365922577619878119…84336116742259210239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

8.873 × 10⁹⁶(97-digit number)

88731845155239756239…68672233484518420479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

1.774 × 10⁹⁷(98-digit number)

17746369031047951247…37344466969036840959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^11 × origin − 1

3.549 × 10⁹⁷(98-digit number)

35492738062095902495…74688933938073681919

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 #3,007,742

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