Block #447,425

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/17/2014, 6:58:53 AM · Difficulty 10.3552 · 6,361,926 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f13ab1bc400b507fdbe0f0410cae2aaa806805ae1a8ce8adc563e52a988cce83

Height

#447,425

Difficulty

10.355245

Transactions

4

Size

2.56 KB

Version

2

Bits

0a5af151

Nonce

78,180

Timestamp

3/17/2014, 6:58:53 AM

Confirmations

6,361,926

Merkle Root

9bbe0eec4235071874f6c08b8518c9a410df18d63fcc6ac1830486ea504160c4
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.

2.549 × 10¹⁰⁰(101-digit number)
25491628929005360892…52671082541033347999
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
2.549 × 10¹⁰⁰(101-digit number)
25491628929005360892…52671082541033347999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
5.098 × 10¹⁰⁰(101-digit number)
50983257858010721784…05342165082066695999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.019 × 10¹⁰¹(102-digit number)
10196651571602144356…10684330164133391999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.039 × 10¹⁰¹(102-digit number)
20393303143204288713…21368660328266783999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.078 × 10¹⁰¹(102-digit number)
40786606286408577427…42737320656533567999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
8.157 × 10¹⁰¹(102-digit number)
81573212572817154854…85474641313067135999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.631 × 10¹⁰²(103-digit number)
16314642514563430970…70949282626134271999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.262 × 10¹⁰²(103-digit number)
32629285029126861941…41898565252268543999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
6.525 × 10¹⁰²(103-digit number)
65258570058253723883…83797130504537087999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.305 × 10¹⁰³(104-digit number)
13051714011650744776…67594261009074175999
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:57,718,874 XPM·at block #6,809,350 · updates every 60s
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