Block #215,600

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/18/2013, 4:52:34 AM · Difficulty 9.9255 · 6,583,889 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4ad58e5ad17c540124bc29e03738dd4f5725046c4df6073ab5b06ecd676996a3

Height

#215,600

Difficulty

9.925508

Transactions

1

Size

4.46 KB

Version

2

Bits

09ecee1f

Nonce

1,164,797,061

Timestamp

10/18/2013, 4:52:34 AM

Confirmations

6,583,889

Merkle Root

b27e6d7fac9db41d96bee0ffe3697cc40e9181c386decf539f0b3171ab9ecfe5
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.

4.082 × 10⁹³(94-digit number)
40826983072724284129…92055573981821050879
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
4.082 × 10⁹³(94-digit number)
40826983072724284129…92055573981821050879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
8.165 × 10⁹³(94-digit number)
81653966145448568259…84111147963642101759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.633 × 10⁹⁴(95-digit number)
16330793229089713651…68222295927284203519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.266 × 10⁹⁴(95-digit number)
32661586458179427303…36444591854568407039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
6.532 × 10⁹⁴(95-digit number)
65323172916358854607…72889183709136814079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.306 × 10⁹⁵(96-digit number)
13064634583271770921…45778367418273628159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.612 × 10⁹⁵(96-digit number)
26129269166543541842…91556734836547256319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.225 × 10⁹⁵(96-digit number)
52258538333087083685…83113469673094512639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.045 × 10⁹⁶(97-digit number)
10451707666617416737…66226939346189025279
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,639,955 XPM·at block #6,799,488 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.