Block #2,660,411

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.

2.317 × 10⁹⁵(96-digit number)

23174447826635292416…06833286945734620481

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

2.317 × 10⁹⁵(96-digit number)

23174447826635292416…06833286945734620481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.634 × 10⁹⁵(96-digit number)

46348895653270584832…13666573891469240961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.269 × 10⁹⁵(96-digit number)

92697791306541169664…27333147782938481921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.853 × 10⁹⁶(97-digit number)

18539558261308233932…54666295565876963841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.707 × 10⁹⁶(97-digit number)

37079116522616467865…09332591131753927681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.415 × 10⁹⁶(97-digit number)

74158233045232935731…18665182263507855361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.483 × 10⁹⁷(98-digit number)

14831646609046587146…37330364527015710721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.966 × 10⁹⁷(98-digit number)

29663293218093174292…74660729054031421441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.932 × 10⁹⁷(98-digit number)

59326586436186348584…49321458108062842881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.186 × 10⁹⁸(99-digit number)

11865317287237269716…98642916216125685761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

2.373 × 10⁹⁸(99-digit number)

23730634574474539433…97285832432251371521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^11 × origin + 1

4.746 × 10⁹⁸(99-digit number)

47461269148949078867…94571664864502743041

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 #2,660,411

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