1. #6,795,6882CC11 primes

    Cunningham 2nd · ⛏️ coinsforall.io

Block #229,800

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/27/2013, 9:58:34 AM · Difficulty 9.9388 · 6,565,889 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3fe745294efdcbce2b62c96f3c18c04e096a8c96dc446bf076775505a28b36d3

Height

#229,800

Difficulty

9.938790

Transactions

4

Size

1.43 KB

Version

2

Bits

09f05488

Nonce

38,080

Timestamp

10/27/2013, 9:58:34 AM

Confirmations

6,565,889

Merkle Root

9b149e9291894292f4fdf4c8d6aa926d87aa01c12ba0c5cfd4c085eb831f83a4
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.

5.928 × 10⁹⁷(98-digit number)
59284131291547213033…15103818531972807681
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
5.928 × 10⁹⁷(98-digit number)
59284131291547213033…15103818531972807681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.185 × 10⁹⁸(99-digit number)
11856826258309442606…30207637063945615361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.371 × 10⁹⁸(99-digit number)
23713652516618885213…60415274127891230721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.742 × 10⁹⁸(99-digit number)
47427305033237770426…20830548255782461441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
9.485 × 10⁹⁸(99-digit number)
94854610066475540853…41661096511564922881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.897 × 10⁹⁹(100-digit number)
18970922013295108170…83322193023129845761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.794 × 10⁹⁹(100-digit number)
37941844026590216341…66644386046259691521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.588 × 10⁹⁹(100-digit number)
75883688053180432682…33288772092519383041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.517 × 10¹⁰⁰(101-digit number)
15176737610636086536…66577544185038766081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.035 × 10¹⁰⁰(101-digit number)
30353475221272173073…33155088370077532161
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:57,609,582 XPM·at block #6,795,688 · updates every 60s
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