Block #861,197

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.

3.239 × 10⁹⁶(97-digit number)

32399795802036765453…45116945125526077439

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

3.239 × 10⁹⁶(97-digit number)

32399795802036765453…45116945125526077439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.479 × 10⁹⁶(97-digit number)

64799591604073530906…90233890251052154879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.295 × 10⁹⁷(98-digit number)

12959918320814706181…80467780502104309759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.591 × 10⁹⁷(98-digit number)

25919836641629412362…60935561004208619519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.183 × 10⁹⁷(98-digit number)

51839673283258824725…21871122008417239039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.036 × 10⁹⁸(99-digit number)

10367934656651764945…43742244016834478079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.073 × 10⁹⁸(99-digit number)

20735869313303529890…87484488033668956159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.147 × 10⁹⁸(99-digit number)

41471738626607059780…74968976067337912319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

8.294 × 10⁹⁸(99-digit number)

82943477253214119560…49937952134675824639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.658 × 10⁹⁹(100-digit number)

16588695450642823912…99875904269351649279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

3.317 × 10⁹⁹(100-digit number)

33177390901285647824…99751808538703298559

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 First 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 1CC formula:

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

Cross-reference on Chainz Explorer