Block #79,730

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/23/2013, 4:54:34 PM · Difficulty 9.2429 · 6,713,308 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

d695255c597581c76c217b958cfce9513c03e1dcf103dbe741a12a0226a28df7

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Height

#79,730

Difficulty

9.242918

Transactions

Size

865 B

Version

Bits

093e2fe3

Nonce

212,404

Timestamp

7/23/2013, 4:54:34 PM

Confirmations

6,713,308

Merkle Root

ad31a79eb639756ac7321d14617c7c28ff23f50e3c6f8b92c793a0f962900fac

Transactions (2)

Coinbasea6f962b33c3a5a…a62b1b8444f52b

1 in → 1 out11.7000 XPM109 B

AKZCZmTp…WY5H7DVV

da77461bdd7b25…73adc0b16f1a0b

4 in → 2 out799.9158 XPM669 B

AZyCQuCh…wJp3kd1X AcU3G17t…7wPGLC6Z

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.

1.998 × 10⁸⁷(88-digit number)

19986451973488164415…35929614344054288651

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

1.998 × 10⁸⁷(88-digit number)

19986451973488164415…35929614344054288651

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.997 × 10⁸⁷(88-digit number)

39972903946976328831…71859228688108577301

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

7.994 × 10⁸⁷(88-digit number)

79945807893952657663…43718457376217154601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.598 × 10⁸⁸(89-digit number)

15989161578790531532…87436914752434309201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.197 × 10⁸⁸(89-digit number)

31978323157581063065…74873829504868618401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

6.395 × 10⁸⁸(89-digit number)

63956646315162126130…49747659009737236801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.279 × 10⁸⁹(90-digit number)

12791329263032425226…99495318019474473601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.558 × 10⁸⁹(90-digit number)

25582658526064850452…98990636038948947201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.116 × 10⁸⁹(90-digit number)

51165317052129700904…97981272077897894401

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