Block #1,230,739

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 9/10/2015, 8:11:52 PM · Difficulty 10.7375 · 5,614,592 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
08ba66b8486772293b2990c7e93edb388d6f9951b3b02c76875d362c7243255f

Height

#1,230,739

Difficulty

10.737456

Transactions

3

Size

1.36 KB

Version

2

Bits

0abcc9e3

Nonce

158,953,821

Timestamp

9/10/2015, 8:11:52 PM

Confirmations

5,614,592

Merkle Root

be89cea08445b2a7b607a5e2f1cf4e2a1e55e9bffb6e184de04a4663c51ea868
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.

1.309 × 10⁹³(94-digit number)
13092688192406724708…18027914142599702079
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
1.309 × 10⁹³(94-digit number)
13092688192406724708…18027914142599702079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.618 × 10⁹³(94-digit number)
26185376384813449416…36055828285199404159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.237 × 10⁹³(94-digit number)
52370752769626898832…72111656570398808319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.047 × 10⁹⁴(95-digit number)
10474150553925379766…44223313140797616639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.094 × 10⁹⁴(95-digit number)
20948301107850759532…88446626281595233279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.189 × 10⁹⁴(95-digit number)
41896602215701519065…76893252563190466559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
8.379 × 10⁹⁴(95-digit number)
83793204431403038131…53786505126380933119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.675 × 10⁹⁵(96-digit number)
16758640886280607626…07573010252761866239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.351 × 10⁹⁵(96-digit number)
33517281772561215252…15146020505523732479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
6.703 × 10⁹⁵(96-digit number)
67034563545122430505…30292041011047464959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.340 × 10⁹⁶(97-digit number)
13406912709024486101…60584082022094929919
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:58,007,089 XPM·at block #6,845,330 · updates every 60s
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