Block #922,348

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 2/4/2015, 10:02:03 AM · Difficulty 10.9155 · 5,869,277 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c13fb4af5b5e878091d28e1c6db639b2e17427b765be38f761f5816936399029

Height

#922,348

Difficulty

10.915549

Transactions

5

Size

115.95 KB

Version

2

Bits

0aea6173

Nonce

668,409,356

Timestamp

2/4/2015, 10:02:03 AM

Confirmations

5,869,277

Merkle Root

e494cfe83f03d1abd37d48798a83ea7e72f9a6cceab1c2148312f327e3aa08e6
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out1125.7653 XPM28.95 KB
200 in → 1 out1002.3235 XPM28.93 KB
200 in → 1 out1009.9699 XPM28.93 KB
200 in → 1 out1072.9376 XPM28.93 KB
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.

1.287 × 10⁹⁵(96-digit number)
12876993410317936608…58067282649368974661
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
1.287 × 10⁹⁵(96-digit number)
12876993410317936608…58067282649368974661
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.575 × 10⁹⁵(96-digit number)
25753986820635873216…16134565298737949321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.150 × 10⁹⁵(96-digit number)
51507973641271746432…32269130597475898641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.030 × 10⁹⁶(97-digit number)
10301594728254349286…64538261194951797281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.060 × 10⁹⁶(97-digit number)
20603189456508698573…29076522389903594561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.120 × 10⁹⁶(97-digit number)
41206378913017397146…58153044779807189121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.241 × 10⁹⁶(97-digit number)
82412757826034794292…16306089559614378241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.648 × 10⁹⁷(98-digit number)
16482551565206958858…32612179119228756481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.296 × 10⁹⁷(98-digit number)
32965103130413917717…65224358238457512961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.593 × 10⁹⁷(98-digit number)
65930206260827835434…30448716476915025921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.318 × 10⁹⁸(99-digit number)
13186041252165567086…60897432953830051841
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:57,576,948 XPM·at block #6,791,624 · updates every 60s
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