Block #485,296

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/10/2014, 11:44:57 PM · Difficulty 10.6063 · 6,340,261 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ced0b6d956e9ea8399c898c861ad578f1c8d06e6eb036fe1535ccde04a10237e

Height

#485,296

Difficulty

10.606310

Transactions

3

Size

954 B

Version

2

Bits

0a9b3722

Nonce

5,405,661

Timestamp

4/10/2014, 11:44:57 PM

Confirmations

6,340,261

Merkle Root

c8d308d1809c717934638cb484aa8c68aeeb8ed11efd8b8fd7e256bc74806102
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.

7.905 × 10⁹³(94-digit number)
79050607447962796766…14325948353466824649
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
7.905 × 10⁹³(94-digit number)
79050607447962796766…14325948353466824649
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.581 × 10⁹⁴(95-digit number)
15810121489592559353…28651896706933649299
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.162 × 10⁹⁴(95-digit number)
31620242979185118706…57303793413867298599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.324 × 10⁹⁴(95-digit number)
63240485958370237413…14607586827734597199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.264 × 10⁹⁵(96-digit number)
12648097191674047482…29215173655469194399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.529 × 10⁹⁵(96-digit number)
25296194383348094965…58430347310938388799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.059 × 10⁹⁵(96-digit number)
50592388766696189930…16860694621876777599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.011 × 10⁹⁶(97-digit number)
10118477753339237986…33721389243753555199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.023 × 10⁹⁶(97-digit number)
20236955506678475972…67442778487507110399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.047 × 10⁹⁶(97-digit number)
40473911013356951944…34885556975014220799
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:57,848,556 XPM·at block #6,825,556 · updates every 60s
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