Block #281,234

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/28/2013, 11:07:11 PM · Difficulty 9.9765 · 6,514,715 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

82b0007009c1961b24c0535b04ad44b12ab7d424d931ef4d9076e494cc26deb4

View on Chainz ↗

Height

#281,234

Difficulty

9.976532

Transactions

Size

1.15 KB

Version

Bits

09f9fdf8

Nonce

53,836

Timestamp

11/28/2013, 11:07:11 PM

Confirmations

6,514,715

Mined by

⛏️ JaRAJ9QW1VPrTJhTox1T8ogp3PGmDGmAJhvhc

Merkle Root

b0e38ed0c077d97b9179c1124b944570b7401671e0a915c3714c5750e0bbbdf4

Transactions (1)

Coinbaseb0e38ed0c077d9…4c5750e0bbbdf4

1 in → 30 out10.0100 XPM1.06 KB

AJ9QW1VP…GmAJhvhc AGFAJ5YL…ZEnBbk6G AN63YyQR…1tfe566A AXz2kWvX…V5ZFCDBd AVui4SmP…9rJrBgX6

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.

2.503 × 10¹⁰³(104-digit number)

25033740041034624922…67966356315152005119

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

2.503 × 10¹⁰³(104-digit number)

25033740041034624922…67966356315152005119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.006 × 10¹⁰³(104-digit number)

50067480082069249844…35932712630304010239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.001 × 10¹⁰⁴(105-digit number)

10013496016413849968…71865425260608020479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.002 × 10¹⁰⁴(105-digit number)

20026992032827699937…43730850521216040959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.005 × 10¹⁰⁴(105-digit number)

40053984065655399875…87461701042432081919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.010 × 10¹⁰⁴(105-digit number)

80107968131310799751…74923402084864163839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.602 × 10¹⁰⁵(106-digit number)

16021593626262159950…49846804169728327679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.204 × 10¹⁰⁵(106-digit number)

32043187252524319900…99693608339456655359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.408 × 10¹⁰⁵(106-digit number)

64086374505048639801…99387216678913310719

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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer