Block #1,342,800

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/26/2015, 2:11:58 PM · Difficulty 10.8107 · 5,452,344 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fa4a0eb7ddf36c5f5b031f19568feb993856960fcc362fe8e86a42299ecbda07

Height

#1,342,800

Difficulty

10.810662

Transactions

3

Size

43.43 KB

Version

2

Bits

0acf878b

Nonce

1,166,304,369

Timestamp

11/26/2015, 2:11:58 PM

Confirmations

5,452,344

Merkle Root

2462631ad8d8a9ba1dd81acd642430568fbdc9a1f712602cdc80137e8e57fd31
Transactions (3)
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.

9.958 × 10⁹⁴(95-digit number)
99588150860558631958…14237899124147799041
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
9.958 × 10⁹⁴(95-digit number)
99588150860558631958…14237899124147799041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.991 × 10⁹⁵(96-digit number)
19917630172111726391…28475798248295598081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.983 × 10⁹⁵(96-digit number)
39835260344223452783…56951596496591196161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.967 × 10⁹⁵(96-digit number)
79670520688446905566…13903192993182392321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.593 × 10⁹⁶(97-digit number)
15934104137689381113…27806385986364784641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.186 × 10⁹⁶(97-digit number)
31868208275378762226…55612771972729569281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.373 × 10⁹⁶(97-digit number)
63736416550757524453…11225543945459138561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.274 × 10⁹⁷(98-digit number)
12747283310151504890…22451087890918277121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.549 × 10⁹⁷(98-digit number)
25494566620303009781…44902175781836554241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.098 × 10⁹⁷(98-digit number)
50989133240606019562…89804351563673108481
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:57,605,193 XPM·at block #6,795,143 · updates every 60s
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