Block #464,539

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/28/2014, 8:34:43 PM · Difficulty 10.4222 · 6,345,320 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
09a901b9bee249f36a9db6530e88529f85d843691d157331b81fd8bb6a5dfa30

Height

#464,539

Difficulty

10.422157

Transactions

1

Size

968 B

Version

2

Bits

0a6c1283

Nonce

190,741

Timestamp

3/28/2014, 8:34:43 PM

Confirmations

6,345,320

Merkle Root

90ec7902368685320b3297f3a1519665a4f7541b886fe50e77dd88756d359f6a
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.

4.856 × 10⁹²(93-digit number)
48565600177360907896…19591301576452097681
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
4.856 × 10⁹²(93-digit number)
48565600177360907896…19591301576452097681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
9.713 × 10⁹²(93-digit number)
97131200354721815792…39182603152904195361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.942 × 10⁹³(94-digit number)
19426240070944363158…78365206305808390721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.885 × 10⁹³(94-digit number)
38852480141888726317…56730412611616781441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
7.770 × 10⁹³(94-digit number)
77704960283777452634…13460825223233562881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.554 × 10⁹⁴(95-digit number)
15540992056755490526…26921650446467125761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.108 × 10⁹⁴(95-digit number)
31081984113510981053…53843300892934251521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.216 × 10⁹⁴(95-digit number)
62163968227021962107…07686601785868503041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.243 × 10⁹⁵(96-digit number)
12432793645404392421…15373203571737006081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.486 × 10⁹⁵(96-digit number)
24865587290808784842…30746407143474012161
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:57,722,960 XPM·at block #6,809,858 · updates every 60s
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