Block #1,173,401

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 7/27/2015, 10:33:44 PM · Difficulty 10.9378 · 5,667,846 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4fd941eb3d0b473e504cec21ed912393366d5bcd471be5595fa6394f81b92b01

Height

#1,173,401

Difficulty

10.937751

Transactions

8

Size

1.61 KB

Version

2

Bits

0af0106c

Nonce

5,297,565

Timestamp

7/27/2015, 10:33:44 PM

Confirmations

5,667,846

Merkle Root

2ae171828b3d8f67f611ecbfa04192851dbdb628a9b99e60db754fbff3f83f05
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.

8.911 × 10⁹⁶(97-digit number)
89113067805774926689…70045327114392832001
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
8.911 × 10⁹⁶(97-digit number)
89113067805774926689…70045327114392832001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.782 × 10⁹⁷(98-digit number)
17822613561154985337…40090654228785664001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.564 × 10⁹⁷(98-digit number)
35645227122309970675…80181308457571328001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.129 × 10⁹⁷(98-digit number)
71290454244619941351…60362616915142656001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.425 × 10⁹⁸(99-digit number)
14258090848923988270…20725233830285312001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.851 × 10⁹⁸(99-digit number)
28516181697847976540…41450467660570624001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.703 × 10⁹⁸(99-digit number)
57032363395695953081…82900935321141248001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.140 × 10⁹⁹(100-digit number)
11406472679139190616…65801870642282496001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.281 × 10⁹⁹(100-digit number)
22812945358278381232…31603741284564992001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.562 × 10⁹⁹(100-digit number)
45625890716556762465…63207482569129984001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
9.125 × 10⁹⁹(100-digit number)
91251781433113524930…26414965138259968001
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,974,338 XPM·at block #6,841,246 · updates every 60s
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