Block #1,461,148

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/17/2016, 9:30:20 AM · Difficulty 10.7790 · 5,383,608 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
68026299ef11518c3971308a0542a7f2165e6132cd28bc71de7f306bccabcd4c

Height

#1,461,148

Difficulty

10.779027

Transactions

2

Size

1.72 KB

Version

2

Bits

0ac76e4a

Nonce

110,470,920

Timestamp

2/17/2016, 9:30:20 AM

Confirmations

5,383,608

Merkle Root

0aea96c9c34a0f95f26f2b51d58354b3070e95d16f911fb31aab8016389b145b
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.

1.328 × 10⁹³(94-digit number)
13288842103319122776…87489693188925049841
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
1.328 × 10⁹³(94-digit number)
13288842103319122776…87489693188925049841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.657 × 10⁹³(94-digit number)
26577684206638245553…74979386377850099681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.315 × 10⁹³(94-digit number)
53155368413276491106…49958772755700199361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.063 × 10⁹⁴(95-digit number)
10631073682655298221…99917545511400398721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.126 × 10⁹⁴(95-digit number)
21262147365310596442…99835091022800797441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.252 × 10⁹⁴(95-digit number)
42524294730621192885…99670182045601594881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.504 × 10⁹⁴(95-digit number)
85048589461242385771…99340364091203189761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.700 × 10⁹⁵(96-digit number)
17009717892248477154…98680728182406379521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.401 × 10⁹⁵(96-digit number)
34019435784496954308…97361456364812759041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.803 × 10⁹⁵(96-digit number)
68038871568993908616…94722912729625518081
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:58,002,463 XPM·at block #6,844,755 · updates every 60s
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