Block #1,372,413

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 12/17/2015, 4:52:13 AM · Difficulty 10.8095 · 5,444,400 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3e54673452c9db304750c810a0ae96961989257acb41a4ec495f38a0fc36d589

Height

#1,372,413

Difficulty

10.809549

Transactions

2

Size

1.57 KB

Version

2

Bits

0acf3e95

Nonce

1,165,745,782

Timestamp

12/17/2015, 4:52:13 AM

Confirmations

5,444,400

Merkle Root

ad809dd0c931c3d6c76fd82dea916b7957d729bb08393a58256ed05b42b084f4
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.

3.290 × 10⁹³(94-digit number)
32907927492454272015…06357422234231218319
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
3.290 × 10⁹³(94-digit number)
32907927492454272015…06357422234231218319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
6.581 × 10⁹³(94-digit number)
65815854984908544031…12714844468462436639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.316 × 10⁹⁴(95-digit number)
13163170996981708806…25429688936924873279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.632 × 10⁹⁴(95-digit number)
26326341993963417612…50859377873849746559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.265 × 10⁹⁴(95-digit number)
52652683987926835225…01718755747699493119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.053 × 10⁹⁵(96-digit number)
10530536797585367045…03437511495398986239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.106 × 10⁹⁵(96-digit number)
21061073595170734090…06875022990797972479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.212 × 10⁹⁵(96-digit number)
42122147190341468180…13750045981595944959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
8.424 × 10⁹⁵(96-digit number)
84244294380682936360…27500091963191889919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.684 × 10⁹⁶(97-digit number)
16848858876136587272…55000183926383779839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
3.369 × 10⁹⁶(97-digit number)
33697717752273174544…10000367852767559679
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:57,778,542 XPM·at block #6,816,812 · updates every 60s
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