Block #2,604,959

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.

1.071 × 10⁹⁵(96-digit number)

10716381373680983933…78548163721219933521

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

1.071 × 10⁹⁵(96-digit number)

10716381373680983933…78548163721219933521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.143 × 10⁹⁵(96-digit number)

21432762747361967867…57096327442439867041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.286 × 10⁹⁵(96-digit number)

42865525494723935734…14192654884879734081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

8.573 × 10⁹⁵(96-digit number)

85731050989447871469…28385309769759468161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.714 × 10⁹⁶(97-digit number)

17146210197889574293…56770619539518936321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.429 × 10⁹⁶(97-digit number)

34292420395779148587…13541239079037872641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.858 × 10⁹⁶(97-digit number)

68584840791558297175…27082478158075745281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.371 × 10⁹⁷(98-digit number)

13716968158311659435…54164956316151490561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.743 × 10⁹⁷(98-digit number)

27433936316623318870…08329912632302981121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

5.486 × 10⁹⁷(98-digit number)

54867872633246637740…16659825264605962241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

1.097 × 10⁹⁸(99-digit number)

10973574526649327548…33319650529211924481

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 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

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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer

Block #2,604,959

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