Block #69,882

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/20/2013, 10:51:50 AM · Difficulty 8.9915 · 6,729,396 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

779636baa694b8e7692da27f7423a71f5502099598a920e3eafac1a125270f3d

View on Chainz ↗

Height

#69,882

Difficulty

8.991500

Transactions

Size

431 B

Version

Bits

08fdd2ec

Nonce

266

Timestamp

7/20/2013, 10:51:50 AM

Confirmations

6,729,396

Mined by

⛏️ P2SHAMrp8sbobqiD6fBANEUucT4Bv5Gf5pxrJR

Merkle Root

f1b79521dc51cc9f8456c3a8377b304a316ed93a72210eb51b625e8437f8b29b

Transactions (2)

Coinbase8baa33dd22a664…0f80bf9a017f8e

1 in → 1 out12.3600 XPM110 B

AMrp8sbo…Gf5pxrJR

cb6d31678457ab…bade7a3b401348

1 in → 2 out12.1258 XPM226 B

AH2vGRVh…AKwkPV5A AVfsJ9sg…CKtUG8Fn

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.

2.459 × 10¹⁰⁷(108-digit number)

24599432852126307107…38234753256436088461

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

2.459 × 10¹⁰⁷(108-digit number)

24599432852126307107…38234753256436088461

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.919 × 10¹⁰⁷(108-digit number)

49198865704252614215…76469506512872176921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.839 × 10¹⁰⁷(108-digit number)

98397731408505228431…52939013025744353841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.967 × 10¹⁰⁸(109-digit number)

19679546281701045686…05878026051488707681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.935 × 10¹⁰⁸(109-digit number)

39359092563402091372…11756052102977415361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.871 × 10¹⁰⁸(109-digit number)

78718185126804182744…23512104205954830721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.574 × 10¹⁰⁹(110-digit number)

15743637025360836548…47024208411909661441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.148 × 10¹⁰⁹(110-digit number)

31487274050721673097…94048416823819322881

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 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 8

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