1. #6,796,7161CC11 primes

    Cunningham 1st · ⛏️ coinsforall.io

Block #904,887

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/22/2015, 6:27:23 AM · Difficulty 10.9365 · 5,891,829 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
34c5cb84aaeee79376c190a876fc2f9e0747112bb4c3d9a812b57ab30c0c25e5

Height

#904,887

Difficulty

10.936451

Transactions

2

Size

1.87 KB

Version

2

Bits

0aefbb45

Nonce

1,614,923,638

Timestamp

1/22/2015, 6:27:23 AM

Confirmations

5,891,829

Merkle Root

9001cdb0f3ea46ff6bfba60c5281db5116891d3b72e06288998efdb77dee0f69
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.

1.813 × 10⁹⁶(97-digit number)
18137550949410023375…62321275017660144001
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
1.813 × 10⁹⁶(97-digit number)
18137550949410023375…62321275017660144001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.627 × 10⁹⁶(97-digit number)
36275101898820046751…24642550035320288001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.255 × 10⁹⁶(97-digit number)
72550203797640093502…49285100070640576001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.451 × 10⁹⁷(98-digit number)
14510040759528018700…98570200141281152001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.902 × 10⁹⁷(98-digit number)
29020081519056037400…97140400282562304001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.804 × 10⁹⁷(98-digit number)
58040163038112074801…94280800565124608001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.160 × 10⁹⁸(99-digit number)
11608032607622414960…88561601130249216001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.321 × 10⁹⁸(99-digit number)
23216065215244829920…77123202260498432001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.643 × 10⁹⁸(99-digit number)
46432130430489659841…54246404520996864001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.286 × 10⁹⁸(99-digit number)
92864260860979319683…08492809041993728001
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:57,617,732 XPM·at block #6,796,715 · updates every 60s
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