Block #862,744

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 12/21/2014, 11:50:28 PM · Difficulty 10.9631 · 5,931,445 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cb3ebb29b694f058f6e9e851cfaaa89d4af3369f1a408c4a0b21afd8829ebfc9

Height

#862,744

Difficulty

10.963104

Transactions

2

Size

728 B

Version

2

Bits

0af68df9

Nonce

383,807,186

Timestamp

12/21/2014, 11:50:28 PM

Confirmations

5,931,445

Merkle Root

b910224ab7ed72094410f051cfc8f1ddb8a0291d0b3c1288b1b84f2c8012e82b
Transactions (2)
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.

7.129 × 10⁹⁷(98-digit number)
71294445445831029196…36675758088645017601
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
7.129 × 10⁹⁷(98-digit number)
71294445445831029196…36675758088645017601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.425 × 10⁹⁸(99-digit number)
14258889089166205839…73351516177290035201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.851 × 10⁹⁸(99-digit number)
28517778178332411678…46703032354580070401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.703 × 10⁹⁸(99-digit number)
57035556356664823356…93406064709160140801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.140 × 10⁹⁹(100-digit number)
11407111271332964671…86812129418320281601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.281 × 10⁹⁹(100-digit number)
22814222542665929342…73624258836640563201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.562 × 10⁹⁹(100-digit number)
45628445085331858685…47248517673281126401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.125 × 10⁹⁹(100-digit number)
91256890170663717370…94497035346562252801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.825 × 10¹⁰⁰(101-digit number)
18251378034132743474…88994070693124505601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.650 × 10¹⁰⁰(101-digit number)
36502756068265486948…77988141386249011201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
7.300 × 10¹⁰⁰(101-digit number)
73005512136530973896…55976282772498022401
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:57,597,535 XPM·at block #6,794,188 · updates every 60s
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