Block #2,113,579

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.

2.146 × 10⁹⁵(96-digit number)

21463586118408128985…15934165428681789599

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

2.146 × 10⁹⁵(96-digit number)

21463586118408128985…15934165428681789599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.292 × 10⁹⁵(96-digit number)

42927172236816257970…31868330857363579199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

8.585 × 10⁹⁵(96-digit number)

85854344473632515940…63736661714727158399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.717 × 10⁹⁶(97-digit number)

17170868894726503188…27473323429454316799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.434 × 10⁹⁶(97-digit number)

34341737789453006376…54946646858908633599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.868 × 10⁹⁶(97-digit number)

68683475578906012752…09893293717817267199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.373 × 10⁹⁷(98-digit number)

13736695115781202550…19786587435634534399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.747 × 10⁹⁷(98-digit number)

27473390231562405101…39573174871269068799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.494 × 10⁹⁷(98-digit number)

54946780463124810202…79146349742538137599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.098 × 10⁹⁸(99-digit number)

10989356092624962040…58292699485076275199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

2.197 × 10⁹⁸(99-digit number)

21978712185249924080…16585398970152550399

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 #2,113,579

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