Block #1,362,451

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/9/2015, 2:09:45 PM · Difficulty 10.8434 · 5,464,206 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c49f8c736126b18c52299d44108575ee6732a9d2851f2d36b2df20d8e3c2cdf7

Height

#1,362,451

Difficulty

10.843443

Transactions

2

Size

836 B

Version

2

Bits

0ad7ebdd

Nonce

1,830,365,052

Timestamp

12/9/2015, 2:09:45 PM

Confirmations

5,464,206

Merkle Root

d81b0a027acfe888f5f4887b5b5a843429ef98165f40ab48a78eec1e35d7ebc7
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.

6.968 × 10⁹⁷(98-digit number)
69688128946823886907…06769770926982266881
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
6.968 × 10⁹⁷(98-digit number)
69688128946823886907…06769770926982266881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.393 × 10⁹⁸(99-digit number)
13937625789364777381…13539541853964533761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.787 × 10⁹⁸(99-digit number)
27875251578729554762…27079083707929067521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.575 × 10⁹⁸(99-digit number)
55750503157459109525…54158167415858135041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.115 × 10⁹⁹(100-digit number)
11150100631491821905…08316334831716270081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.230 × 10⁹⁹(100-digit number)
22300201262983643810…16632669663432540161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.460 × 10⁹⁹(100-digit number)
44600402525967287620…33265339326865080321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.920 × 10⁹⁹(100-digit number)
89200805051934575241…66530678653730160641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.784 × 10¹⁰⁰(101-digit number)
17840161010386915048…33061357307460321281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.568 × 10¹⁰⁰(101-digit number)
35680322020773830096…66122714614920642561
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:57,857,406 XPM·at block #6,826,656 · updates every 60s
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