1. #6,816,692TWN11 primes

    Bi-Twin · ⛏️ coinsforall.io

Block #374,216

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/24/2014, 8:51:10 PM · Difficulty 10.4259 · 6,442,477 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0526e7053c5a6920574147984262c8262106012a61f12b4269ed3ed6aa325f79

Height

#374,216

Difficulty

10.425856

Transactions

3

Size

659 B

Version

2

Bits

0a6d04ed

Nonce

16,778,207

Timestamp

1/24/2014, 8:51:10 PM

Confirmations

6,442,477

Merkle Root

ff282269bd6fde7580f7ec90560176d7d709bd0bbc34b01255776a66557fef77
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.

3.579 × 10⁹⁶(97-digit number)
35790438365771839872…33747634583345721599
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
3.579 × 10⁹⁶(97-digit number)
35790438365771839872…33747634583345721599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.158 × 10⁹⁶(97-digit number)
71580876731543679745…67495269166691443199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.431 × 10⁹⁷(98-digit number)
14316175346308735949…34990538333382886399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.863 × 10⁹⁷(98-digit number)
28632350692617471898…69981076666765772799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.726 × 10⁹⁷(98-digit number)
57264701385234943796…39962153333531545599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.145 × 10⁹⁸(99-digit number)
11452940277046988759…79924306667063091199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.290 × 10⁹⁸(99-digit number)
22905880554093977518…59848613334126182399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.581 × 10⁹⁸(99-digit number)
45811761108187955036…19697226668252364799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
9.162 × 10⁹⁸(99-digit number)
91623522216375910073…39394453336504729599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.832 × 10⁹⁹(100-digit number)
18324704443275182014…78788906673009459199
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:57,777,666 XPM·at block #6,816,692 · updates every 60s
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