Block #1,389,584

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/29/2015, 2:54:09 AM · Difficulty 10.8105 · 5,451,810 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2ca4f6f4aee37d9e8b4de6944826c8605e5414fc49be1fa390651c38ae212340

Height

#1,389,584

Difficulty

10.810488

Transactions

2

Size

1018 B

Version

2

Bits

0acf7c1e

Nonce

192,104,715

Timestamp

12/29/2015, 2:54:09 AM

Confirmations

5,451,810

Merkle Root

9b18015bae39af41262da687604fcc6d092900b5b9f2f010e5476ac12d34f282
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.

5.920 × 10⁹⁴(95-digit number)
59204745042757158900…55501953414153347921
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
5.920 × 10⁹⁴(95-digit number)
59204745042757158900…55501953414153347921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.184 × 10⁹⁵(96-digit number)
11840949008551431780…11003906828306695841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.368 × 10⁹⁵(96-digit number)
23681898017102863560…22007813656613391681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.736 × 10⁹⁵(96-digit number)
47363796034205727120…44015627313226783361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
9.472 × 10⁹⁵(96-digit number)
94727592068411454240…88031254626453566721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.894 × 10⁹⁶(97-digit number)
18945518413682290848…76062509252907133441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.789 × 10⁹⁶(97-digit number)
37891036827364581696…52125018505814266881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.578 × 10⁹⁶(97-digit number)
75782073654729163392…04250037011628533761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.515 × 10⁹⁷(98-digit number)
15156414730945832678…08500074023257067521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.031 × 10⁹⁷(98-digit number)
30312829461891665357…17000148046514135041
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,975,524 XPM·at block #6,841,393 · updates every 60s
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