Block #1,546,743

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/18/2016, 10:07:04 AM · Difficulty 10.6564 · 5,279,906 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4bb9bdb869ca117f6aa17b8a61488f987bd176ec811f034afb76851b09ee5360

Height

#1,546,743

Difficulty

10.656413

Transactions

2

Size

799 B

Version

2

Bits

0aa80ab0

Nonce

1,309,320,000

Timestamp

4/18/2016, 10:07:04 AM

Confirmations

5,279,906

Merkle Root

76c148bb039d559b2c041791c3f7170fd80a077b694011ce22dc4388de76d32e
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.

4.108 × 10⁹²(93-digit number)
41082498020311031793…55202317848970969601
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
4.108 × 10⁹²(93-digit number)
41082498020311031793…55202317848970969601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.216 × 10⁹²(93-digit number)
82164996040622063586…10404635697941939201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.643 × 10⁹³(94-digit number)
16432999208124412717…20809271395883878401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.286 × 10⁹³(94-digit number)
32865998416248825434…41618542791767756801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.573 × 10⁹³(94-digit number)
65731996832497650869…83237085583535513601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.314 × 10⁹⁴(95-digit number)
13146399366499530173…66474171167071027201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.629 × 10⁹⁴(95-digit number)
26292798732999060347…32948342334142054401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.258 × 10⁹⁴(95-digit number)
52585597465998120695…65896684668284108801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.051 × 10⁹⁵(96-digit number)
10517119493199624139…31793369336568217601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.103 × 10⁹⁵(96-digit number)
21034238986399248278…63586738673136435201
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:57,857,341 XPM·at block #6,826,648 · updates every 60s
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