1. #6,806,153TWN11 primes

    Bi-Twin · ⛏️ coinsforall.io

Block #1,534,802

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/10/2016, 11:49:27 AM · Difficulty 10.6184 · 5,271,352 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
eb865fbd2d1e34390365f2df9a580a9130bf25270dad184c6d4fea195e1fb3fc

Height

#1,534,802

Difficulty

10.618387

Transactions

3

Size

15.02 KB

Version

2

Bits

0a9e4ea0

Nonce

143,086,700

Timestamp

4/10/2016, 11:49:27 AM

Confirmations

5,271,352

Merkle Root

33d18d243534cbb88d590fbb080e89942e84ccf2c0af30c8c79f32bb7f4781db
Transactions (3)
1 in → 1 out9.0200 XPM109 B
51 in → 1 out1514.2563 XPM7.41 KB
51 in → 1 out763.2076 XPM7.41 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.

1.314 × 10⁹²(93-digit number)
13140621548205584222…99103716877217802521
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
1.314 × 10⁹²(93-digit number)
13140621548205584222…99103716877217802521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.628 × 10⁹²(93-digit number)
26281243096411168445…98207433754435605041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.256 × 10⁹²(93-digit number)
52562486192822336891…96414867508871210081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.051 × 10⁹³(94-digit number)
10512497238564467378…92829735017742420161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.102 × 10⁹³(94-digit number)
21024994477128934756…85659470035484840321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.204 × 10⁹³(94-digit number)
42049988954257869513…71318940070969680641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.409 × 10⁹³(94-digit number)
84099977908515739026…42637880141939361281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.681 × 10⁹⁴(95-digit number)
16819995581703147805…85275760283878722561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.363 × 10⁹⁴(95-digit number)
33639991163406295610…70551520567757445121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.727 × 10⁹⁴(95-digit number)
67279982326812591221…41103041135514890241
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:57,693,312 XPM·at block #6,806,153 · updates every 60s
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