Block #1,705,929

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.

4.081 × 10⁹⁴(95-digit number)

40819989878254649690…74196729966739403449

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

4.081 × 10⁹⁴(95-digit number)

40819989878254649690…74196729966739403449

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

8.163 × 10⁹⁴(95-digit number)

81639979756509299381…48393459933478806899

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.632 × 10⁹⁵(96-digit number)

16327995951301859876…96786919866957613799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.265 × 10⁹⁵(96-digit number)

32655991902603719752…93573839733915227599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.531 × 10⁹⁵(96-digit number)

65311983805207439504…87147679467830455199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.306 × 10⁹⁶(97-digit number)

13062396761041487900…74295358935660910399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.612 × 10⁹⁶(97-digit number)

26124793522082975801…48590717871321820799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.224 × 10⁹⁶(97-digit number)

52249587044165951603…97181435742643641599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.044 × 10⁹⁷(98-digit number)

10449917408833190320…94362871485287283199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.089 × 10⁹⁷(98-digit number)

20899834817666380641…88725742970574566399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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