Block #848,476

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 12/11/2014, 2:58:09 AM · Difficulty 10.9716 · 5,996,465 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4eaea94d88ddc4dd159e1b4870756ef98df977ac49f4bda3997fc77707f6fdf3

Height

#848,476

Difficulty

10.971575

Transactions

3

Size

726 B

Version

2

Bits

0af8b927

Nonce

2,216,198,569

Timestamp

12/11/2014, 2:58:09 AM

Confirmations

5,996,465

Merkle Root

9e07e9a981ed3002578393b7915131e260f20e2b2f6e3109c26bb956a381b5ad
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.

1.464 × 10⁹⁷(98-digit number)
14645005122144760175…25197907193712279041
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
1.464 × 10⁹⁷(98-digit number)
14645005122144760175…25197907193712279041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.929 × 10⁹⁷(98-digit number)
29290010244289520351…50395814387424558081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.858 × 10⁹⁷(98-digit number)
58580020488579040702…00791628774849116161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.171 × 10⁹⁸(99-digit number)
11716004097715808140…01583257549698232321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.343 × 10⁹⁸(99-digit number)
23432008195431616280…03166515099396464641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.686 × 10⁹⁸(99-digit number)
46864016390863232561…06333030198792929281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
9.372 × 10⁹⁸(99-digit number)
93728032781726465123…12666060397585858561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.874 × 10⁹⁹(100-digit number)
18745606556345293024…25332120795171717121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.749 × 10⁹⁹(100-digit number)
37491213112690586049…50664241590343434241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.498 × 10⁹⁹(100-digit number)
74982426225381172098…01328483180686868481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.499 × 10¹⁰⁰(101-digit number)
14996485245076234419…02656966361373736961
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:58,003,947 XPM·at block #6,844,940 · updates every 60s
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