Block #250,958

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/8/2013, 6:16:30 PM · Difficulty 9.9692 · 6,555,120 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

bab7ef5584f17cfab90e1085c69cc1b988eb73ef559a10ea482ee104e68dddf7

View on Chainz ↗

Height

#250,958

Difficulty

9.969210

Transactions

Size

1.58 KB

Version

Bits

09f81e2a

Nonce

3,922

Timestamp

11/8/2013, 6:16:30 PM

Confirmations

6,555,120

Mined by

⛏️ NaR}ARpndEmcGyFUFhdFVbgqJiPBAmHg792kEk

Merkle Root

4be400fef34053e90e2c58bcde315d3a777f9a1b4ae03da25a96f2339e948e60

Transactions (1)

Coinbase4be400fef34053…96f2339e948e60

1 in → 43 out10.0300 XPM1.49 KB

ARpndEmc…Hg792kEk AFqKfjez…qX9Ace3g AQtzUSwq…htAuF3yC AJKYzp1g…SvZiepke AUS2k1RS…EcDna3ZF

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.

2.628 × 10⁹⁴(95-digit number)

26289400508619618132…06396643024671508479

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

2.628 × 10⁹⁴(95-digit number)

26289400508619618132…06396643024671508479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.257 × 10⁹⁴(95-digit number)

52578801017239236265…12793286049343016959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.051 × 10⁹⁵(96-digit number)

10515760203447847253…25586572098686033919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.103 × 10⁹⁵(96-digit number)

21031520406895694506…51173144197372067839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.206 × 10⁹⁵(96-digit number)

42063040813791389012…02346288394744135679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.412 × 10⁹⁵(96-digit number)

84126081627582778025…04692576789488271359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.682 × 10⁹⁶(97-digit number)

16825216325516555605…09385153578976542719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.365 × 10⁹⁶(97-digit number)

33650432651033111210…18770307157953085439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.730 × 10⁹⁶(97-digit number)

67300865302066222420…37540614315906170879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.346 × 10⁹⁷(98-digit number)

13460173060413244484…75081228631812341759

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