Block #1,496,626

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/14/2016, 5:08:03 PM · Difficulty 10.6445 · 5,328,797 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c3020653c345a150693dc03293cfba86cea54854b23c55551ece01ec70d49637

Height

#1,496,626

Difficulty

10.644517

Transactions

2

Size

1.38 KB

Version

2

Bits

0aa4ff14

Nonce

49,618,294

Timestamp

3/14/2016, 5:08:03 PM

Confirmations

5,328,797

Merkle Root

d736f537cee141441fea75185046c4baf3c215c8d772937245e2b4d225b2b1f5
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.

7.548 × 10⁹³(94-digit number)
75480726979272132275…54837317260977700641
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
7.548 × 10⁹³(94-digit number)
75480726979272132275…54837317260977700641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.509 × 10⁹⁴(95-digit number)
15096145395854426455…09674634521955401281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.019 × 10⁹⁴(95-digit number)
30192290791708852910…19349269043910802561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.038 × 10⁹⁴(95-digit number)
60384581583417705820…38698538087821605121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.207 × 10⁹⁵(96-digit number)
12076916316683541164…77397076175643210241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.415 × 10⁹⁵(96-digit number)
24153832633367082328…54794152351286420481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.830 × 10⁹⁵(96-digit number)
48307665266734164656…09588304702572840961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.661 × 10⁹⁵(96-digit number)
96615330533468329312…19176609405145681921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.932 × 10⁹⁶(97-digit number)
19323066106693665862…38353218810291363841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.864 × 10⁹⁶(97-digit number)
38646132213387331724…76706437620582727681
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:57,847,485 XPM·at block #6,825,422 · updates every 60s
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