Block #630,604

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 7/13/2014, 2:01:23 AM · Difficulty 10.9614 · 6,178,514 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
da8a0016fe6c4c6bce11c3d6c435dbea298c4a17c05a2b94cb4b4cc8a722f4cc

Height

#630,604

Difficulty

10.961420

Transactions

1

Size

494 B

Version

2

Bits

0af61f9f

Nonce

6,622

Timestamp

7/13/2014, 2:01:23 AM

Confirmations

6,178,514

Merkle Root

fe047110f9b2a4533d0f48741521ff6a8b9b7e8334685cfc1adec7f774823c23
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.

1.201 × 10¹⁰⁰(101-digit number)
12018261428801776070…68446439138413478399
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
1.201 × 10¹⁰⁰(101-digit number)
12018261428801776070…68446439138413478399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.403 × 10¹⁰⁰(101-digit number)
24036522857603552140…36892878276826956799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.807 × 10¹⁰⁰(101-digit number)
48073045715207104280…73785756553653913599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
9.614 × 10¹⁰⁰(101-digit number)
96146091430414208561…47571513107307827199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.922 × 10¹⁰¹(102-digit number)
19229218286082841712…95143026214615654399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.845 × 10¹⁰¹(102-digit number)
38458436572165683424…90286052429231308799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
7.691 × 10¹⁰¹(102-digit number)
76916873144331366849…80572104858462617599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.538 × 10¹⁰²(103-digit number)
15383374628866273369…61144209716925235199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.076 × 10¹⁰²(103-digit number)
30766749257732546739…22288419433850470399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
6.153 × 10¹⁰²(103-digit number)
61533498515465093479…44576838867700940799
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,717,001 XPM·at block #6,809,117 · updates every 60s
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