Block #271,484

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/24/2013, 4:07:07 PM · Difficulty 9.9519 · 6,521,589 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

7f34d8903a5c26058db7c4508ad46a2acd51c68594e5b467e10d41b3e7eb19eb

View on Chainz ↗

Height

#271,484

Difficulty

9.951896

Transactions

Size

835 B

Version

Bits

09f3af7b

Nonce

6,694

Timestamp

11/24/2013, 4:07:07 PM

Confirmations

6,521,589

Merkle Root

53c20f3a207e4196b552d5248389af3a9a68082b92590ce45f0d87ae257eb93a

Transactions (3)

Coinbaseb2ae772c4c7f94…fbd196bd5395a2

1 in → 2 out10.1000 XPM141 B

AKcbk49N…GJbKa7j1 AU6kq4CL…dQBLvxLp

8a417e960f8ee8…488484bd22956f

2 in → 2 out1.4866 XPM374 B

AXSwSKcF…4w2v6rXz AQQEZrze…wgfK19Fz

0455bdbb5806be…9e2bf1b56ba5d9

1 in → 2 out8.0395 XPM227 B

ANikdk3c…VB96aPGe ANUPa5nC…gS5uF4Pm

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.

1.553 × 10¹⁰²(103-digit number)

15536924359553813951…69087974643829542681

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

1.553 × 10¹⁰²(103-digit number)

15536924359553813951…69087974643829542681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.107 × 10¹⁰²(103-digit number)

31073848719107627902…38175949287659085361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.214 × 10¹⁰²(103-digit number)

62147697438215255805…76351898575318170721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.242 × 10¹⁰³(104-digit number)

12429539487643051161…52703797150636341441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.485 × 10¹⁰³(104-digit number)

24859078975286102322…05407594301272682881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.971 × 10¹⁰³(104-digit number)

49718157950572204644…10815188602545365761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.943 × 10¹⁰³(104-digit number)

99436315901144409288…21630377205090731521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.988 × 10¹⁰⁴(105-digit number)

19887263180228881857…43260754410181463041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.977 × 10¹⁰⁴(105-digit number)

39774526360457763715…86521508820362926081

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