Block #1,371,768

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 12/16/2015, 5:38:34 PM · Difficulty 10.8107 · 5,446,012 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9e229a4ac86ce728353fe7000805029243e1a6f552d090e74485e76aca8f8c63

Height

#1,371,768

Difficulty

10.810663

Transactions

2

Size

1.43 KB

Version

2

Bits

0acf8794

Nonce

525,746,553

Timestamp

12/16/2015, 5:38:34 PM

Confirmations

5,446,012

Merkle Root

9c6308af94310c1bdbf7ba40dcb0d394fe62511cfaa3a184847dba56ac69f073
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.

4.428 × 10⁹⁵(96-digit number)
44281666424900796289…02538549336867782321
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
4.428 × 10⁹⁵(96-digit number)
44281666424900796289…02538549336867782321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.856 × 10⁹⁵(96-digit number)
88563332849801592579…05077098673735564641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.771 × 10⁹⁶(97-digit number)
17712666569960318515…10154197347471129281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.542 × 10⁹⁶(97-digit number)
35425333139920637031…20308394694942258561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
7.085 × 10⁹⁶(97-digit number)
70850666279841274063…40616789389884517121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.417 × 10⁹⁷(98-digit number)
14170133255968254812…81233578779769034241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.834 × 10⁹⁷(98-digit number)
28340266511936509625…62467157559538068481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.668 × 10⁹⁷(98-digit number)
56680533023873019250…24934315119076136961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.133 × 10⁹⁸(99-digit number)
11336106604774603850…49868630238152273921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.267 × 10⁹⁸(99-digit number)
22672213209549207700…99737260476304547841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
4.534 × 10⁹⁸(99-digit number)
45344426419098415400…99474520952609095681
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:57,786,299 XPM·at block #6,817,779 · updates every 60s
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