1. #6,827,222TWN10 primes

    Bi-Twin · ⛏️ coinsforall.io

Block #2,160,489

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/14/2017, 3:19:20 PM · Difficulty 10.9015 · 4,666,734 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e9d34cb471cd4600831093a9e1451ac579787ccad0d9c46cf7d6f34c56620dfd

Height

#2,160,489

Difficulty

10.901529

Transactions

3

Size

8.39 KB

Version

2

Bits

0ae6ca98

Nonce

493,680,045

Timestamp

6/14/2017, 3:19:20 PM

Confirmations

4,666,734

Merkle Root

43c2be201dbb6a92d699aab6309474830ac1b48dcd61243a4b33c241fcf4af72
Transactions (3)
1 in → 1 out8.5000 XPM109 B
35 in → 1 out1187.5380 XPM5.09 KB
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.

3.818 × 10⁹⁵(96-digit number)
38182795213168290556…95149960429692962561
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
3.818 × 10⁹⁵(96-digit number)
38182795213168290556…95149960429692962561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.636 × 10⁹⁵(96-digit number)
76365590426336581112…90299920859385925121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.527 × 10⁹⁶(97-digit number)
15273118085267316222…80599841718771850241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.054 × 10⁹⁶(97-digit number)
30546236170534632444…61199683437543700481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.109 × 10⁹⁶(97-digit number)
61092472341069264889…22399366875087400961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.221 × 10⁹⁷(98-digit number)
12218494468213852977…44798733750174801921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.443 × 10⁹⁷(98-digit number)
24436988936427705955…89597467500349603841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.887 × 10⁹⁷(98-digit number)
48873977872855411911…79194935000699207681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.774 × 10⁹⁷(98-digit number)
97747955745710823823…58389870001398415361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.954 × 10⁹⁸(99-digit number)
19549591149142164764…16779740002796830721
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:57,861,882 XPM·at block #6,827,222 · updates every 60s
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