Block #1,113,262

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 6/17/2015, 2:53:08 PM · Difficulty 10.9032 · 5,694,366 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
87b130d9371095a91daa49802b5816763c570d56a9395342f7912f86800a875b

Height

#1,113,262

Difficulty

10.903196

Transactions

3

Size

2.95 KB

Version

2

Bits

0ae737d3

Nonce

268,776,062

Timestamp

6/17/2015, 2:53:08 PM

Confirmations

5,694,366

Merkle Root

885231b6f4af05905c34b9a0bd0d11052d5af780bc24106cd4267a55b3fe75ac
Transactions (3)
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.

1.470 × 10⁹⁴(95-digit number)
14703371869298377323…92647086766578127679
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
1.470 × 10⁹⁴(95-digit number)
14703371869298377323…92647086766578127679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.940 × 10⁹⁴(95-digit number)
29406743738596754646…85294173533156255359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.881 × 10⁹⁴(95-digit number)
58813487477193509293…70588347066312510719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.176 × 10⁹⁵(96-digit number)
11762697495438701858…41176694132625021439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.352 × 10⁹⁵(96-digit number)
23525394990877403717…82353388265250042879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.705 × 10⁹⁵(96-digit number)
47050789981754807434…64706776530500085759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
9.410 × 10⁹⁵(96-digit number)
94101579963509614869…29413553061000171519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.882 × 10⁹⁶(97-digit number)
18820315992701922973…58827106122000343039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.764 × 10⁹⁶(97-digit number)
37640631985403845947…17654212244000686079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
7.528 × 10⁹⁶(97-digit number)
75281263970807691895…35308424488001372159
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, …
Circulating Supply:57,705,049 XPM·at block #6,807,627 · updates every 60s
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