Block #261,430

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/15/2013, 5:10:28 PM · Difficulty 9.9724 · 6,541,245 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

658a3bdbe84afb7b034c06a2ae2b543eb3bc902c90709b154d2d2ee3fe687150

View on Chainz ↗

Height

#261,430

Difficulty

9.972389

Transactions

Size

1.81 KB

Version

Bits

09f8ee7f

Nonce

361,855

Timestamp

11/15/2013, 5:10:28 PM

Confirmations

6,541,245

Mined by

⛏️ 6aRT`EALvH9UXBP3Wydd6TiZ8rV3L1fEheQe1BX8

Merkle Root

7733336935ff502f5b832e98c3d0c7af6f06f14bfa879736045755a3a5acf948

Transactions (1)

Coinbase7733336935ff50…5755a3a5acf948

1 in → 50 out10.0200 XPM1.72 KB

ALvH9UXB…heQe1BX8 AFqKfjez…qX9Ace3g APH8rV6F…heb1HF2Z AQtzUSwq…htAuF3yC ANsrD1P6…m3RxY4uj

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.

1.040 × 10⁹¹(92-digit number)

10409579038577042853…99883266528674262919

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

1.040 × 10⁹¹(92-digit number)

10409579038577042853…99883266528674262919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.081 × 10⁹¹(92-digit number)

20819158077154085707…99766533057348525839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.163 × 10⁹¹(92-digit number)

41638316154308171415…99533066114697051679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

8.327 × 10⁹¹(92-digit number)

83276632308616342830…99066132229394103359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.665 × 10⁹²(93-digit number)

16655326461723268566…98132264458788206719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.331 × 10⁹²(93-digit number)

33310652923446537132…96264528917576413439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.662 × 10⁹²(93-digit number)

66621305846893074264…92529057835152826879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.332 × 10⁹³(94-digit number)

13324261169378614852…85058115670305653759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.664 × 10⁹³(94-digit number)

26648522338757229705…70116231340611307519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

5.329 × 10⁹³(94-digit number)

53297044677514459411…40232462681222615039

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