Block #88,607

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/29/2013, 6:26:07 PM · Difficulty 9.2649 · 6,703,219 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

4d77275c56a8884437d526b7d92e9737c7da9a76b2bde8b48c48236acce5c799

View on Chainz ↗

Height

#88,607

Difficulty

9.264873

Transactions

Size

205 B

Version

Bits

0943ceb9

Nonce

155,242

Timestamp

7/29/2013, 6:26:07 PM

Confirmations

6,703,219

Merkle Root

7a8ddfc6e5aed38d20a64707691401885c5ce9533c858a362271d8c20851ce50

Transactions (1)

Coinbase7a8ddfc6e5aed3…71d8c20851ce50

1 in → 1 out11.6300 XPM109 B

ASXW8s4r…LM8vqY9U

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.

5.315 × 10¹⁰⁹(110-digit number)

53155960579457577094…91127723636011973621

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

5.315 × 10¹⁰⁹(110-digit number)

53155960579457577094…91127723636011973621

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.063 × 10¹¹⁰(111-digit number)

10631192115891515418…82255447272023947241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.126 × 10¹¹⁰(111-digit number)

21262384231783030837…64510894544047894481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.252 × 10¹¹⁰(111-digit number)

42524768463566061675…29021789088095788961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

8.504 × 10¹¹⁰(111-digit number)

85049536927132123351…58043578176191577921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.700 × 10¹¹¹(112-digit number)

17009907385426424670…16087156352383155841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.401 × 10¹¹¹(112-digit number)

34019814770852849340…32174312704766311681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

6.803 × 10¹¹¹(112-digit number)

68039629541705698680…64348625409532623361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.360 × 10¹¹²(113-digit number)

13607925908341139736…28697250819065246721

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