Block #2,275,433

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.

1.386 × 10⁹⁶(97-digit number)

13867425680508386565…51085510366458448641

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

1.386 × 10⁹⁶(97-digit number)

13867425680508386565…51085510366458448641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.773 × 10⁹⁶(97-digit number)

27734851361016773131…02171020732916897281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.546 × 10⁹⁶(97-digit number)

55469702722033546263…04342041465833794561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.109 × 10⁹⁷(98-digit number)

11093940544406709252…08684082931667589121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.218 × 10⁹⁷(98-digit number)

22187881088813418505…17368165863335178241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.437 × 10⁹⁷(98-digit number)

44375762177626837011…34736331726670356481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

8.875 × 10⁹⁷(98-digit number)

88751524355253674022…69472663453340712961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.775 × 10⁹⁸(99-digit number)

17750304871050734804…38945326906681425921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.550 × 10⁹⁸(99-digit number)

35500609742101469608…77890653813362851841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

7.100 × 10⁹⁸(99-digit number)

71001219484202939217…55781307626725703681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

1.420 × 10⁹⁹(100-digit number)

14200243896840587843…11562615253451407361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^11 × origin + 1

2.840 × 10⁹⁹(100-digit number)

28400487793681175687…23125230506902814721

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 #2,275,433

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