Block #1,566,403

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/30/2016, 9:03:23 PM · Difficulty 10.7565 · 5,260,323 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a94009887b31907cd2549fee04840bc67e13c742b20de94daa5c130a45bf31fa

Height

#1,566,403

Difficulty

10.756544

Transactions

2

Size

902 B

Version

2

Bits

0ac1acd7

Nonce

1,323,807,935

Timestamp

4/30/2016, 9:03:23 PM

Confirmations

5,260,323

Merkle Root

1bab39200cca59412a41f54732809da63bac59404706d704481846ab507756d8
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.

8.964 × 10⁹⁴(95-digit number)
89643578032217822945…39894843382541925121
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
8.964 × 10⁹⁴(95-digit number)
89643578032217822945…39894843382541925121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.792 × 10⁹⁵(96-digit number)
17928715606443564589…79789686765083850241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.585 × 10⁹⁵(96-digit number)
35857431212887129178…59579373530167700481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.171 × 10⁹⁵(96-digit number)
71714862425774258356…19158747060335400961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.434 × 10⁹⁶(97-digit number)
14342972485154851671…38317494120670801921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.868 × 10⁹⁶(97-digit number)
28685944970309703342…76634988241341603841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.737 × 10⁹⁶(97-digit number)
57371889940619406684…53269976482683207681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.147 × 10⁹⁷(98-digit number)
11474377988123881336…06539952965366415361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.294 × 10⁹⁷(98-digit number)
22948755976247762673…13079905930732830721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.589 × 10⁹⁷(98-digit number)
45897511952495525347…26159811861465661441
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:57,857,961 XPM·at block #6,826,725 · updates every 60s
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