Block #2,682,938

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.

2.718 × 10⁹⁴(95-digit number)

27180280568623548484…50631672360046126081

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

2.718 × 10⁹⁴(95-digit number)

27180280568623548484…50631672360046126081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.436 × 10⁹⁴(95-digit number)

54360561137247096968…01263344720092252161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.087 × 10⁹⁵(96-digit number)

10872112227449419393…02526689440184504321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.174 × 10⁹⁵(96-digit number)

21744224454898838787…05053378880369008641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.348 × 10⁹⁵(96-digit number)

43488448909797677574…10106757760738017281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

8.697 × 10⁹⁵(96-digit number)

86976897819595355148…20213515521476034561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.739 × 10⁹⁶(97-digit number)

17395379563919071029…40427031042952069121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.479 × 10⁹⁶(97-digit number)

34790759127838142059…80854062085904138241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.958 × 10⁹⁶(97-digit number)

69581518255676284119…61708124171808276481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.391 × 10⁹⁷(98-digit number)

13916303651135256823…23416248343616552961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

2.783 × 10⁹⁷(98-digit number)

27832607302270513647…46832496687233105921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^11 × origin + 1

5.566 × 10⁹⁷(98-digit number)

55665214604541027295…93664993374466211841

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 #2,682,938

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