Block #2,632,848

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 4/28/2018, 2:23:27 AM · Difficulty 11.1772 · 4,212,296 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6612ab83df7366d8e9b0c5456fd6dcded6a3435181a302c3657f136c7e2d9e2e

Height

#2,632,848

Difficulty

11.177226

Transactions

2

Size

576 B

Version

2

Bits

0b2d5eab

Nonce

774,508,627

Timestamp

4/28/2018, 2:23:27 AM

Confirmations

4,212,296

Merkle Root

166ea0851dba5677ad99e87481a24361df5f600d9d7ae925d59b3f8ad41553b4
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.

1.509 × 10⁹⁶(97-digit number)
15094338096311305475…27859763538703948799
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
1.509 × 10⁹⁶(97-digit number)
15094338096311305475…27859763538703948799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.018 × 10⁹⁶(97-digit number)
30188676192622610951…55719527077407897599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.037 × 10⁹⁶(97-digit number)
60377352385245221903…11439054154815795199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.207 × 10⁹⁷(98-digit number)
12075470477049044380…22878108309631590399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.415 × 10⁹⁷(98-digit number)
24150940954098088761…45756216619263180799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.830 × 10⁹⁷(98-digit number)
48301881908196177522…91512433238526361599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
9.660 × 10⁹⁷(98-digit number)
96603763816392355045…83024866477052723199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.932 × 10⁹⁸(99-digit number)
19320752763278471009…66049732954105446399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.864 × 10⁹⁸(99-digit number)
38641505526556942018…32099465908210892799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
7.728 × 10⁹⁸(99-digit number)
77283011053113884036…64198931816421785599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.545 × 10⁹⁹(100-digit number)
15456602210622776807…28397863632843571199
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:58,005,580 XPM·at block #6,845,143 · updates every 60s
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