1. #6,809,957TWN11 primes

    Bi-Twin · ⛏️ coinsforall.io

Block #479,089

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/7/2014, 11:57:42 AM · Difficulty 10.4999 · 6,330,869 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c1a8c8ddbfb605e380b757642d76239abf358b51831342ea726ca419b449e436

Height

#479,089

Difficulty

10.499941

Transactions

1

Size

970 B

Version

2

Bits

0a7ffc22

Nonce

85,953

Timestamp

4/7/2014, 11:57:42 AM

Confirmations

6,330,869

Merkle Root

cefe742e1cf052a9be371331a719e1256db9c3f15a462323e9ac626ee64f7498
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.

2.689 × 10⁹⁷(98-digit number)
26893135688725212060…77305138020747524159
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
2.689 × 10⁹⁷(98-digit number)
26893135688725212060…77305138020747524159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
5.378 × 10⁹⁷(98-digit number)
53786271377450424120…54610276041495048319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.075 × 10⁹⁸(99-digit number)
10757254275490084824…09220552082990096639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.151 × 10⁹⁸(99-digit number)
21514508550980169648…18441104165980193279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.302 × 10⁹⁸(99-digit number)
43029017101960339296…36882208331960386559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
8.605 × 10⁹⁸(99-digit number)
86058034203920678592…73764416663920773119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.721 × 10⁹⁹(100-digit number)
17211606840784135718…47528833327841546239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.442 × 10⁹⁹(100-digit number)
34423213681568271436…95057666655683092479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
6.884 × 10⁹⁹(100-digit number)
68846427363136542873…90115333311366184959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.376 × 10¹⁰⁰(101-digit number)
13769285472627308574…80230666622732369919
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 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
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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,723,737 XPM·at block #6,809,957 · updates every 60s
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