1. #6,808,3011CC11 primes

    Cunningham 1st · ⛏️ coinsforall.io

  2. #6,808,300TWN11 primes

    Bi-Twin · ⛏️ coinsforall.io

Block #1,226,722

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/8/2015, 1:56:00 AM · Difficulty 10.7351 · 5,581,579 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1d0d7b974b12d6c74e9986134cee8b03322acd8721c60ccc3c27efc9004235a3

Height

#1,226,722

Difficulty

10.735066

Transactions

3

Size

798 B

Version

2

Bits

0abc2d47

Nonce

1,610,268,289

Timestamp

9/8/2015, 1:56:00 AM

Confirmations

5,581,579

Merkle Root

7146c4f4bdf0007bbfd27be4903895e1d17dea60a50eb9d2189885f4880b60b4
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.

8.332 × 10⁹⁴(95-digit number)
83321033220346556622…84238699006948139601
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
8.332 × 10⁹⁴(95-digit number)
83321033220346556622…84238699006948139601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.666 × 10⁹⁵(96-digit number)
16664206644069311324…68477398013896279201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.332 × 10⁹⁵(96-digit number)
33328413288138622648…36954796027792558401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.665 × 10⁹⁵(96-digit number)
66656826576277245297…73909592055585116801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.333 × 10⁹⁶(97-digit number)
13331365315255449059…47819184111170233601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.666 × 10⁹⁶(97-digit number)
26662730630510898119…95638368222340467201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.332 × 10⁹⁶(97-digit number)
53325461261021796238…91276736444680934401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.066 × 10⁹⁷(98-digit number)
10665092252204359247…82553472889361868801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.133 × 10⁹⁷(98-digit number)
21330184504408718495…65106945778723737601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.266 × 10⁹⁷(98-digit number)
42660369008817436990…30213891557447475201
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:57,710,462 XPM·at block #6,808,300 · updates every 60s
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