Block #88,162

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/29/2013, 10:06:56 AM · Difficulty 9.2727 · 6,701,778 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

a44b1fb2432eb743ca5567b92b0071616afd1043d60be54b4d136a90da0d4e8b

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Height

#88,162

Difficulty

9.272686

Transactions

Size

206 B

Version

Bits

0945cec4

Nonce

14,148

Timestamp

7/29/2013, 10:06:56 AM

Confirmations

6,701,778

Merkle Root

98c2fe132a7681be6722e4b0df815535e588855e61205f87308ed60f49da533d

Transactions (1)

Coinbase98c2fe132a7681…8ed60f49da533d

1 in → 1 out11.6100 XPM109 B

AK1JUKWL…oPR4rN5o

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.

1.029 × 10¹¹¹(112-digit number)

10296019012024259994…66341148004217685101

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

1.029 × 10¹¹¹(112-digit number)

10296019012024259994…66341148004217685101

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.059 × 10¹¹¹(112-digit number)

20592038024048519988…32682296008435370201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.118 × 10¹¹¹(112-digit number)

41184076048097039977…65364592016870740401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

8.236 × 10¹¹¹(112-digit number)

82368152096194079955…30729184033741480801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.647 × 10¹¹²(113-digit number)

16473630419238815991…61458368067482961601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.294 × 10¹¹²(113-digit number)

32947260838477631982…22916736134965923201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.589 × 10¹¹²(113-digit number)

65894521676955263964…45833472269931846401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.317 × 10¹¹³(114-digit number)

13178904335391052792…91666944539863692801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.635 × 10¹¹³(114-digit number)

26357808670782105585…83333889079727385601

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 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

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 2CC formula:

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

Cross-reference on Chainz Explorer