Block #2,476,384

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/16/2018, 11:07:42 PM · Difficulty 10.9645 · 4,362,805 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
62df7e941ec9ff77d774eb102a510904706523d4b2c3b9eb50ac0f21d473721a

Height

#2,476,384

Difficulty

10.964452

Transactions

16

Size

8.40 KB

Version

2

Bits

0af6e64c

Nonce

52,786,105

Timestamp

1/16/2018, 11:07:42 PM

Confirmations

4,362,805

Merkle Root

bdc4f009ed5c61db4ac886ee3b5b9b7ecd8e8aaa0c4cffaa96768598c16f77d0
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.

1.643 × 10⁹⁶(97-digit number)
16430324651960012242…79639049828461211521
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
1.643 × 10⁹⁶(97-digit number)
16430324651960012242…79639049828461211521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.286 × 10⁹⁶(97-digit number)
32860649303920024484…59278099656922423041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
6.572 × 10⁹⁶(97-digit number)
65721298607840048969…18556199313844846081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.314 × 10⁹⁷(98-digit number)
13144259721568009793…37112398627689692161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.628 × 10⁹⁷(98-digit number)
26288519443136019587…74224797255379384321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.257 × 10⁹⁷(98-digit number)
52577038886272039175…48449594510758768641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.051 × 10⁹⁸(99-digit number)
10515407777254407835…96899189021517537281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.103 × 10⁹⁸(99-digit number)
21030815554508815670…93798378043035074561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.206 × 10⁹⁸(99-digit number)
42061631109017631340…87596756086070149121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
8.412 × 10⁹⁸(99-digit number)
84123262218035262681…75193512172140298241
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:57,957,789 XPM·at block #6,839,188 · updates every 60s
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