Block #92,137

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/1/2013, 11:58:22 AM · Difficulty 9.2044 · 6,698,845 confirmations

1CC

Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header

Block Hash

caae9a1ccbb20319ba33646b7688680bdabafa5d4b7310e7dbb208efe1140bfc

View on Chainz ↗

Height

#92,137

Difficulty

9.204448

Transactions

Size

546 B

Version

Bits

093456b7

Nonce

297,995

Timestamp

8/1/2013, 11:58:22 AM

Confirmations

6,698,845

Merkle Root

4f8b6148b0871a252edfd4ae0dc800067e1247f77d31b26ba62f24ded9e6bafe

Transactions (2)

Coinbase686af4c01878ba…acd39c3bb2346b

1 in → 1 out11.8000 XPM109 B

AcBadmkp…GmhL921o

4e6e1800936abe…8183f53823b600

2 in → 1 out120.0100 XPM341 B

AR6HT7bn…jUFDat5r

Prime Chain Origin

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.

1.353 × 10¹⁰⁹(110-digit number)

13531885164187160031…40177728035198347219

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

1.353 × 10¹⁰⁹(110-digit number)

13531885164187160031…40177728035198347219

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.706 × 10¹⁰⁹(110-digit number)

27063770328374320063…80355456070396694439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.412 × 10¹⁰⁹(110-digit number)

54127540656748640127…60710912140793388879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.082 × 10¹¹⁰(111-digit number)

10825508131349728025…21421824281586777759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.165 × 10¹¹⁰(111-digit number)

21651016262699456050…42843648563173555519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.330 × 10¹¹⁰(111-digit number)

43302032525398912101…85687297126347111039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

8.660 × 10¹¹⁰(111-digit number)

86604065050797824203…71374594252694222079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.732 × 10¹¹¹(112-digit number)

17320813010159564840…42749188505388444159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.464 × 10¹¹¹(112-digit number)

34641626020319129681…85498377010776888319

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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