Block #2,929,729

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.

6.599 × 10⁹²(93-digit number)

65998064181569604085…78233635192080216919

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

6.599 × 10⁹²(93-digit number)

65998064181569604085…78233635192080216919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.319 × 10⁹³(94-digit number)

13199612836313920817…56467270384160433839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.639 × 10⁹³(94-digit number)

26399225672627841634…12934540768320867679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.279 × 10⁹³(94-digit number)

52798451345255683268…25869081536641735359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.055 × 10⁹⁴(95-digit number)

10559690269051136653…51738163073283470719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.111 × 10⁹⁴(95-digit number)

21119380538102273307…03476326146566941439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.223 × 10⁹⁴(95-digit number)

42238761076204546614…06952652293133882879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.447 × 10⁹⁴(95-digit number)

84477522152409093229…13905304586267765759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.689 × 10⁹⁵(96-digit number)

16895504430481818645…27810609172535531519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.379 × 10⁹⁵(96-digit number)

33791008860963637291…55621218345071063039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

6.758 × 10⁹⁵(96-digit number)

67582017721927274583…11242436690142126079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^11 × origin − 1

1.351 × 10⁹⁶(97-digit number)

13516403544385454916…22484873380284252159

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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

Block #2,929,729

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