1. #6,831,702TWN10 primes

    Bi-Twin · ⛏️ coinsforall.io

Block #1,714,779

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/13/2016, 4:22:25 AM · Difficulty 10.6566 · 5,116,924 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
98b4d5c04588793e9b1b55bee5d54ba9682b77c9867622ae47f704f2303f42ea

Height

#1,714,779

Difficulty

10.656599

Transactions

1

Size

242 B

Version

2

Bits

0aa816dd

Nonce

295,809,978

Timestamp

8/13/2016, 4:22:25 AM

Confirmations

5,116,924

Merkle Root

4fc8810376ce84282d7e8e261743159712d025d51f94c08ebf0bede262715f9d
Transactions (1)
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.

3.645 × 10⁹⁵(96-digit number)
36458151773444628479…94017227815896184481
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
3.645 × 10⁹⁵(96-digit number)
36458151773444628479…94017227815896184481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.291 × 10⁹⁵(96-digit number)
72916303546889256958…88034455631792368961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.458 × 10⁹⁶(97-digit number)
14583260709377851391…76068911263584737921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.916 × 10⁹⁶(97-digit number)
29166521418755702783…52137822527169475841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.833 × 10⁹⁶(97-digit number)
58333042837511405566…04275645054338951681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.166 × 10⁹⁷(98-digit number)
11666608567502281113…08551290108677903361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.333 × 10⁹⁷(98-digit number)
23333217135004562226…17102580217355806721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.666 × 10⁹⁷(98-digit number)
46666434270009124453…34205160434711613441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.333 × 10⁹⁷(98-digit number)
93332868540018248906…68410320869423226881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.866 × 10⁹⁸(99-digit number)
18666573708003649781…36820641738846453761
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:57,897,733 XPM·at block #6,831,702 · updates every 60s
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