Block #149,522

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 9/4/2013, 10:27:52 AM · Difficulty 9.8574 · 6,667,575 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
da86fbc906e070881c07b5196d951a15d05c03230c5eec456cf871f52b8336a1

Height

#149,522

Difficulty

9.857374

Transactions

2

Size

426 B

Version

2

Bits

09db7cde

Nonce

149,921

Timestamp

9/4/2013, 10:27:52 AM

Confirmations

6,667,575

Merkle Root

53f9f138990437dc9097000fd7a0bc9ecba55780ead5bf40320ce658823f4fe6
Transactions (2)
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.

5.940 × 10⁹³(94-digit number)
59403331102182394044…46510421202602878979
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.

1
origin − 1
5.940 × 10⁹³(94-digit number)
59403331102182394044…46510421202602878979
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.188 × 10⁹⁴(95-digit number)
11880666220436478808…93020842405205757959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.376 × 10⁹⁴(95-digit number)
23761332440872957617…86041684810411515919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.752 × 10⁹⁴(95-digit number)
47522664881745915235…72083369620823031839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
9.504 × 10⁹⁴(95-digit number)
95045329763491830471…44166739241646063679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.900 × 10⁹⁵(96-digit number)
19009065952698366094…88333478483292127359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.801 × 10⁹⁵(96-digit number)
38018131905396732188…76666956966584254719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.603 × 10⁹⁵(96-digit number)
76036263810793464377…53333913933168509439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.520 × 10⁹⁶(97-digit number)
15207252762158692875…06667827866337018879
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, …
Circulating Supply:57,780,813 XPM·at block #6,817,096 · updates every 60s
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