Block #837,143

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.

2.927 × 10⁹⁵(96-digit number)

29278285377785038531…16144605593914519001

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

2.927 × 10⁹⁵(96-digit number)

29278285377785038531…16144605593914519001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.855 × 10⁹⁵(96-digit number)

58556570755570077062…32289211187829038001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.171 × 10⁹⁶(97-digit number)

11711314151114015412…64578422375658076001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.342 × 10⁹⁶(97-digit number)

23422628302228030824…29156844751316152001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.684 × 10⁹⁶(97-digit number)

46845256604456061649…58313689502632304001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.369 × 10⁹⁶(97-digit number)

93690513208912123299…16627379005264608001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.873 × 10⁹⁷(98-digit number)

18738102641782424659…33254758010529216001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.747 × 10⁹⁷(98-digit number)

37476205283564849319…66509516021058432001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.495 × 10⁹⁷(98-digit number)

74952410567129698639…33019032042116864001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.499 × 10⁹⁸(99-digit number)

14990482113425939727…66038064084233728001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

2.998 × 10⁹⁸(99-digit number)

29980964226851879455…32076128168467456001

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 #837,143

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