Block #1,182,966

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 8/4/2015, 10:43:32 PM · Difficulty 10.9084 · 5,633,772 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
86122fc714e971d5945275bd445cfccfe8a893215ade880f2372d954d2fa8944

Height

#1,182,966

Difficulty

10.908422

Transactions

2

Size

879 B

Version

2

Bits

0ae88e55

Nonce

137,721,565

Timestamp

8/4/2015, 10:43:32 PM

Confirmations

5,633,772

Merkle Root

eda8fe7a4dbf4f911c9c92fb8db983ecb4bf224ae8f821a663040b52930f4841
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.

3.112 × 10⁹⁶(97-digit number)
31121705455493204471…61143621229778175999
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
3.112 × 10⁹⁶(97-digit number)
31121705455493204471…61143621229778175999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
6.224 × 10⁹⁶(97-digit number)
62243410910986408943…22287242459556351999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.244 × 10⁹⁷(98-digit number)
12448682182197281788…44574484919112703999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.489 × 10⁹⁷(98-digit number)
24897364364394563577…89148969838225407999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.979 × 10⁹⁷(98-digit number)
49794728728789127154…78297939676450815999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
9.958 × 10⁹⁷(98-digit number)
99589457457578254309…56595879352901631999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.991 × 10⁹⁸(99-digit number)
19917891491515650861…13191758705803263999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.983 × 10⁹⁸(99-digit number)
39835782983031301723…26383517411606527999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
7.967 × 10⁹⁸(99-digit number)
79671565966062603447…52767034823213055999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.593 × 10⁹⁹(100-digit number)
15934313193212520689…05534069646426111999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
3.186 × 10⁹⁹(100-digit number)
31868626386425041379…11068139292852223999
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:57,777,940 XPM·at block #6,816,737 · updates every 60s
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