Block #480,187

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/8/2014, 3:59:48 AM · Difficulty 10.5140 · 6,329,511 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
446d64ce8c6afc33f07b631ff1eb21bbcb3ea8fb1d5c0096f506219ae25694e2

Height

#480,187

Difficulty

10.514030

Transactions

1

Size

970 B

Version

2

Bits

0a839776

Nonce

10,947

Timestamp

4/8/2014, 3:59:48 AM

Confirmations

6,329,511

Merkle Root

d38a139a91c73b46f6bd00d1552857f522fa32cf0ccf2a625b21b35be8e12b00
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.

2.445 × 10⁹⁷(98-digit number)
24452583967860479918…22617897814321336321
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
2.445 × 10⁹⁷(98-digit number)
24452583967860479918…22617897814321336321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.890 × 10⁹⁷(98-digit number)
48905167935720959837…45235795628642672641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.781 × 10⁹⁷(98-digit number)
97810335871441919675…90471591257285345281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.956 × 10⁹⁸(99-digit number)
19562067174288383935…80943182514570690561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.912 × 10⁹⁸(99-digit number)
39124134348576767870…61886365029141381121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.824 × 10⁹⁸(99-digit number)
78248268697153535740…23772730058282762241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.564 × 10⁹⁹(100-digit number)
15649653739430707148…47545460116565524481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.129 × 10⁹⁹(100-digit number)
31299307478861414296…95090920233131048961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.259 × 10⁹⁹(100-digit number)
62598614957722828592…90181840466262097921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.251 × 10¹⁰⁰(101-digit number)
12519722991544565718…80363680932524195841
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:57,721,661 XPM·at block #6,809,697 · updates every 60s
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