Block #2,757,721

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.

2.461 × 10⁹⁷(98-digit number)

24611194519760940540…82183048031256514561

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

2.461 × 10⁹⁷(98-digit number)

24611194519760940540…82183048031256514561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.922 × 10⁹⁷(98-digit number)

49222389039521881081…64366096062513029121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.844 × 10⁹⁷(98-digit number)

98444778079043762163…28732192125026058241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.968 × 10⁹⁸(99-digit number)

19688955615808752432…57464384250052116481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.937 × 10⁹⁸(99-digit number)

39377911231617504865…14928768500104232961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.875 × 10⁹⁸(99-digit number)

78755822463235009730…29857537000208465921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.575 × 10⁹⁹(100-digit number)

15751164492647001946…59715074000416931841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.150 × 10⁹⁹(100-digit number)

31502328985294003892…19430148000833863681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.300 × 10⁹⁹(100-digit number)

63004657970588007784…38860296001667727361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.260 × 10¹⁰⁰(101-digit number)

12600931594117601556…77720592003335454721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

2.520 × 10¹⁰⁰(101-digit number)

25201863188235203113…55441184006670909441

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 #2,757,721

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