Block #1,443,362

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/5/2016, 8:04:41 AM · Difficulty 10.7592 · 5,396,311 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
79a4cc6c26fb952ffd5fc4f11156eccfb7a0496baacc14c3d2a49fb8a5811b1e

Height

#1,443,362

Difficulty

10.759224

Transactions

2

Size

936 B

Version

2

Bits

0ac25c7e

Nonce

355,605,955

Timestamp

2/5/2016, 8:04:41 AM

Confirmations

5,396,311

Merkle Root

5727f7704db42dd6b6a8aea621456ce7d2d9ad027d6af3407dedebbbfd07f09c
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.

1.873 × 10⁹⁵(96-digit number)
18737452111995569629…32698739481014471041
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
1.873 × 10⁹⁵(96-digit number)
18737452111995569629…32698739481014471041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.747 × 10⁹⁵(96-digit number)
37474904223991139258…65397478962028942081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.494 × 10⁹⁵(96-digit number)
74949808447982278516…30794957924057884161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.498 × 10⁹⁶(97-digit number)
14989961689596455703…61589915848115768321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.997 × 10⁹⁶(97-digit number)
29979923379192911406…23179831696231536641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.995 × 10⁹⁶(97-digit number)
59959846758385822813…46359663392463073281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.199 × 10⁹⁷(98-digit number)
11991969351677164562…92719326784926146561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.398 × 10⁹⁷(98-digit number)
23983938703354329125…85438653569852293121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.796 × 10⁹⁷(98-digit number)
47967877406708658250…70877307139704586241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.593 × 10⁹⁷(98-digit number)
95935754813417316500…41754614279409172481
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:57,961,673 XPM·at block #6,839,672 · updates every 60s
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