Block #485,018

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/10/2014, 8:18:54 PM · Difficulty 10.6005 · 6,326,084 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c9b14ad1392e42c57eb9300a4435941cc6cecffb92af6e259d9081ab5f7d152c

Height

#485,018

Difficulty

10.600493

Transactions

5

Size

3.59 KB

Version

2

Bits

0a99b9eb

Nonce

11,345,760

Timestamp

4/10/2014, 8:18:54 PM

Confirmations

6,326,084

Merkle Root

1e4e8ae4aa633e0bbb966a1bc153cc255c048652d84ce5c1cc06547a17af9280
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.

4.364 × 10⁹⁶(97-digit number)
43642824659996341844…47374339710169405441
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
4.364 × 10⁹⁶(97-digit number)
43642824659996341844…47374339710169405441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.728 × 10⁹⁶(97-digit number)
87285649319992683689…94748679420338810881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.745 × 10⁹⁷(98-digit number)
17457129863998536737…89497358840677621761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.491 × 10⁹⁷(98-digit number)
34914259727997073475…78994717681355243521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.982 × 10⁹⁷(98-digit number)
69828519455994146951…57989435362710487041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.396 × 10⁹⁸(99-digit number)
13965703891198829390…15978870725420974081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.793 × 10⁹⁸(99-digit number)
27931407782397658780…31957741450841948161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.586 × 10⁹⁸(99-digit number)
55862815564795317561…63915482901683896321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.117 × 10⁹⁹(100-digit number)
11172563112959063512…27830965803367792641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.234 × 10⁹⁹(100-digit number)
22345126225918127024…55661931606735585281
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:57,732,925 XPM·at block #6,811,101 · updates every 60s
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