Block #1,524,392

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/3/2016, 10:04:45 AM · Difficulty 10.6000 · 5,289,833 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1708294f5751767280ece234755cc4c3a495d49a4edabe18227106c077951849

Height

#1,524,392

Difficulty

10.600040

Transactions

2

Size

1.15 KB

Version

2

Bits

0a999c3f

Nonce

464,462,220

Timestamp

4/3/2016, 10:04:45 AM

Confirmations

5,289,833

Merkle Root

680a70b421025896e143db98c51d58a65f10a43ecf631d2746e01cd6b54c051c
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.

5.102 × 10⁹³(94-digit number)
51020972649860510258…36704440295201964241
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
5.102 × 10⁹³(94-digit number)
51020972649860510258…36704440295201964241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.020 × 10⁹⁴(95-digit number)
10204194529972102051…73408880590403928481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.040 × 10⁹⁴(95-digit number)
20408389059944204103…46817761180807856961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.081 × 10⁹⁴(95-digit number)
40816778119888408206…93635522361615713921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.163 × 10⁹⁴(95-digit number)
81633556239776816413…87271044723231427841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.632 × 10⁹⁵(96-digit number)
16326711247955363282…74542089446462855681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.265 × 10⁹⁵(96-digit number)
32653422495910726565…49084178892925711361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.530 × 10⁹⁵(96-digit number)
65306844991821453131…98168357785851422721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.306 × 10⁹⁶(97-digit number)
13061368998364290626…96336715571702845441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.612 × 10⁹⁶(97-digit number)
26122737996728581252…92673431143405690881
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:57,757,870 XPM·at block #6,814,224 · updates every 60s
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