Block #1,426,943

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/25/2016, 12:08:29 AM · Difficulty 10.7536 · 5,413,000 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
aaec387f1cb5fb637b35f8c8db5c9d32889156b07af04c8aad8bd4446eab1047

Height

#1,426,943

Difficulty

10.753647

Transactions

2

Size

698 B

Version

2

Bits

0ac0eefc

Nonce

502,675,803

Timestamp

1/25/2016, 12:08:29 AM

Confirmations

5,413,000

Merkle Root

83ee966d6b1a6ef3efa8485af05198a942e1fea5f80175a1da1045dfb8c2f0e4
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.

1.236 × 10⁹⁵(96-digit number)
12367583995290101987…13187340993501908801
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
1.236 × 10⁹⁵(96-digit number)
12367583995290101987…13187340993501908801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.473 × 10⁹⁵(96-digit number)
24735167990580203975…26374681987003817601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.947 × 10⁹⁵(96-digit number)
49470335981160407951…52749363974007635201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.894 × 10⁹⁵(96-digit number)
98940671962320815902…05498727948015270401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.978 × 10⁹⁶(97-digit number)
19788134392464163180…10997455896030540801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.957 × 10⁹⁶(97-digit number)
39576268784928326360…21994911792061081601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.915 × 10⁹⁶(97-digit number)
79152537569856652721…43989823584122163201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.583 × 10⁹⁷(98-digit number)
15830507513971330544…87979647168244326401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.166 × 10⁹⁷(98-digit number)
31661015027942661088…75959294336488652801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.332 × 10⁹⁷(98-digit number)
63322030055885322177…51918588672977305601
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:57,963,844 XPM·at block #6,839,942 · updates every 60s
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