Block #262,178

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/16/2013, 1:50:36 PM · Difficulty 9.9696 · 6,533,199 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

c66f5711bee0c921939abde9c1716f47f470dd5e5804dd3b167dcbc78d5e4b79

View on Chainz ↗

Height

#262,178

Difficulty

9.969625

Transactions

Size

1.61 KB

Version

Bits

09f8395e

Nonce

6,748

Timestamp

11/16/2013, 1:50:36 PM

Confirmations

6,533,199

Mined by

⛏️ "aRxAQDGVS66x4YUbhY3Z3fTFJcuAE1PTWdWkm

Merkle Root

72b3fbf6ca63d64e44ea4dca854f4b8280deff2556a5aeb06863c77b88f06663

Transactions (1)

Coinbase72b3fbf6ca63d6…63c77b88f06663

1 in → 44 out10.0295 XPM1.52 KB

AQDGVS66…1PTWdWkm AFqKfjez…qX9Ace3g AQtzUSwq…htAuF3yC ANsrD1P6…m3RxY4uj ANHbaxZp…XjnHCJJs

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.

2.981 × 10⁹³(94-digit number)

29810264135875277295…37743370716031261639

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

2.981 × 10⁹³(94-digit number)

29810264135875277295…37743370716031261639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.962 × 10⁹³(94-digit number)

59620528271750554590…75486741432062523279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.192 × 10⁹⁴(95-digit number)

11924105654350110918…50973482864125046559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.384 × 10⁹⁴(95-digit number)

23848211308700221836…01946965728250093119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.769 × 10⁹⁴(95-digit number)

47696422617400443672…03893931456500186239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.539 × 10⁹⁴(95-digit number)

95392845234800887344…07787862913000372479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.907 × 10⁹⁵(96-digit number)

19078569046960177468…15575725826000744959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.815 × 10⁹⁵(96-digit number)

38157138093920354937…31151451652001489919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.631 × 10⁹⁵(96-digit number)

76314276187840709875…62302903304002979839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.526 × 10⁹⁶(97-digit number)

15262855237568141975…24605806608005959679

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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