Block #484,523

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/10/2014, 2:22:27 PM · Difficulty 10.5892 · 6,342,235 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f6ad6d9b355ad41a0672faf60a278d063ad03f6893876acf4c85ba5a2e6ee1d2

Height

#484,523

Difficulty

10.589206

Transactions

3

Size

653 B

Version

2

Bits

0a96d635

Nonce

637,488,002

Timestamp

4/10/2014, 2:22:27 PM

Confirmations

6,342,235

Merkle Root

6a74a4460925556ccc19bda76185a11f6c43b5fbff95d422d743f303222eab6d
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.

2.310 × 10⁹⁷(98-digit number)
23107653856042482690…58469714798153301441
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
2.310 × 10⁹⁷(98-digit number)
23107653856042482690…58469714798153301441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.621 × 10⁹⁷(98-digit number)
46215307712084965380…16939429596306602881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.243 × 10⁹⁷(98-digit number)
92430615424169930760…33878859192613205761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.848 × 10⁹⁸(99-digit number)
18486123084833986152…67757718385226411521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.697 × 10⁹⁸(99-digit number)
36972246169667972304…35515436770452823041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.394 × 10⁹⁸(99-digit number)
73944492339335944608…71030873540905646081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.478 × 10⁹⁹(100-digit number)
14788898467867188921…42061747081811292161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.957 × 10⁹⁹(100-digit number)
29577796935734377843…84123494163622584321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.915 × 10⁹⁹(100-digit number)
59155593871468755686…68246988327245168641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.183 × 10¹⁰⁰(101-digit number)
11831118774293751137…36493976654490337281
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:57,858,223 XPM·at block #6,826,757 · updates every 60s
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