Block #88,672

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/29/2013, 7:27:13 PM · Difficulty 9.2656 · 6,702,266 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

d775aa6a85a4a8aba5fbb32880dd47a1befb4e5342bca5f4b94bc80b319a447a

View on Chainz ↗

Height

#88,672

Difficulty

9.265568

Transactions

Size

1.07 KB

Version

Bits

0943fc40

Nonce

261,070

Timestamp

7/29/2013, 7:27:13 PM

Confirmations

6,702,266

Merkle Root

2e1fedab37a7956cc755e35827b427eca63a0fb0b694656e3efc3fa5bebd065e

Transactions (3)

Coinbase9f7c4c7c853304…a929467098cede

1 in → 1 out11.6500 XPM109 B

AR3ERsDP…fuc7v3x5

2001350bf3947e…4f6ddf0214307c

1 in → 2 out11.5600 XPM226 B

AHyHEeYQ…XuELsExj AXQGgS98…12BLaWMv

86b64aa934ed74…0febe9eed76a79

4 in → 2 out2.0653 XPM669 B

AdnJA43N…SRdVK7xk AHpkvQhU…wp9MgYDu

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.

1.933 × 10¹⁰⁹(110-digit number)

19339070272149926637…00209094483433946861

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

1.933 × 10¹⁰⁹(110-digit number)

19339070272149926637…00209094483433946861

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.867 × 10¹⁰⁹(110-digit number)

38678140544299853275…00418188966867893721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

7.735 × 10¹⁰⁹(110-digit number)

77356281088599706550…00836377933735787441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.547 × 10¹¹⁰(111-digit number)

15471256217719941310…01672755867471574881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.094 × 10¹¹⁰(111-digit number)

30942512435439882620…03345511734943149761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

6.188 × 10¹¹⁰(111-digit number)

61885024870879765240…06691023469886299521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.237 × 10¹¹¹(112-digit number)

12377004974175953048…13382046939772599041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.475 × 10¹¹¹(112-digit number)

24754009948351906096…26764093879545198081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.950 × 10¹¹¹(112-digit number)

49508019896703812192…53528187759090396161

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