Block #1,411,044

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/13/2016, 3:05:50 AM · Difficulty 10.8054 · 5,431,136 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9c810ed95ca2808750813889543169fa5b95c3758e1e7023081e42ea40534a62

Height

#1,411,044

Difficulty

10.805403

Transactions

2

Size

764 B

Version

2

Bits

0ace2eeb

Nonce

574,500,754

Timestamp

1/13/2016, 3:05:50 AM

Confirmations

5,431,136

Merkle Root

b84b6851835082c7a3c2f4f0466fbe72a9ff98e510c72cbf8649f2dfc8afdc11
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.

1.574 × 10⁹⁵(96-digit number)
15744801663235221371…05287458353145967361
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
1.574 × 10⁹⁵(96-digit number)
15744801663235221371…05287458353145967361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.148 × 10⁹⁵(96-digit number)
31489603326470442742…10574916706291934721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
6.297 × 10⁹⁵(96-digit number)
62979206652940885484…21149833412583869441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.259 × 10⁹⁶(97-digit number)
12595841330588177096…42299666825167738881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.519 × 10⁹⁶(97-digit number)
25191682661176354193…84599333650335477761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.038 × 10⁹⁶(97-digit number)
50383365322352708387…69198667300670955521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.007 × 10⁹⁷(98-digit number)
10076673064470541677…38397334601341911041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.015 × 10⁹⁷(98-digit number)
20153346128941083355…76794669202683822081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.030 × 10⁹⁷(98-digit number)
40306692257882166710…53589338405367644161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
8.061 × 10⁹⁷(98-digit number)
80613384515764333420…07178676810735288321
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:57,981,832 XPM·at block #6,842,179 · updates every 60s
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