Block #1,432,553

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/28/2016, 9:29:23 AM · Difficulty 10.7869 · 5,410,350 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7902ca7be9709260d8f386456be4c90d962b53155ed6c2723109ec564d2df5e8

Height

#1,432,553

Difficulty

10.786870

Transactions

4

Size

1.98 KB

Version

2

Bits

0ac97051

Nonce

369,466,606

Timestamp

1/28/2016, 9:29:23 AM

Confirmations

5,410,350

Merkle Root

1567d5c689b66ebb97accb0162adea652775a10a3e78d6168bc60693caf32eb2
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.

6.273 × 10⁹¹(92-digit number)
62735191312319882730…74781324948514880541
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
6.273 × 10⁹¹(92-digit number)
62735191312319882730…74781324948514880541
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.254 × 10⁹²(93-digit number)
12547038262463976546…49562649897029761081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.509 × 10⁹²(93-digit number)
25094076524927953092…99125299794059522161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.018 × 10⁹²(93-digit number)
50188153049855906184…98250599588119044321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.003 × 10⁹³(94-digit number)
10037630609971181236…96501199176238088641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.007 × 10⁹³(94-digit number)
20075261219942362473…93002398352476177281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.015 × 10⁹³(94-digit number)
40150522439884724947…86004796704952354561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.030 × 10⁹³(94-digit number)
80301044879769449895…72009593409904709121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.606 × 10⁹⁴(95-digit number)
16060208975953889979…44019186819809418241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.212 × 10⁹⁴(95-digit number)
32120417951907779958…88038373639618836481
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:57,987,571 XPM·at block #6,842,902 · updates every 60s
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