Block #2,467,956

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/11/2018, 11:13:16 AM · Difficulty 10.9604 · 4,377,338 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d1fb1f6d8fc48564d096d11f579374914834e0c3d105416f76b8fca556b80958

Height

#2,467,956

Difficulty

10.960370

Transactions

2

Size

393 B

Version

2

Bits

0af5dad7

Nonce

313,266,777

Timestamp

1/11/2018, 11:13:16 AM

Confirmations

4,377,338

Merkle Root

d59e8b310fcb1dc04148495bf808c02ec698b8960e0bfb64c14169016559cb85
Transactions (2)
1 in → 1 out8.3200 XPM110 B
1 in → 1 out1999.9900 XPM192 B
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.

9.255 × 10⁹⁵(96-digit number)
92557155686547420146…35884193181130848001
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
9.255 × 10⁹⁵(96-digit number)
92557155686547420146…35884193181130848001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.851 × 10⁹⁶(97-digit number)
18511431137309484029…71768386362261696001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.702 × 10⁹⁶(97-digit number)
37022862274618968058…43536772724523392001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.404 × 10⁹⁶(97-digit number)
74045724549237936117…87073545449046784001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.480 × 10⁹⁷(98-digit number)
14809144909847587223…74147090898093568001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.961 × 10⁹⁷(98-digit number)
29618289819695174446…48294181796187136001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.923 × 10⁹⁷(98-digit number)
59236579639390348893…96588363592374272001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.184 × 10⁹⁸(99-digit number)
11847315927878069778…93176727184748544001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.369 × 10⁹⁸(99-digit number)
23694631855756139557…86353454369497088001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.738 × 10⁹⁸(99-digit number)
47389263711512279115…72706908738994176001
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:58,006,790 XPM·at block #6,845,293 · updates every 60s
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