Block #479,256

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/7/2014, 2:02:32 PM · Difficulty 10.5039 · 6,346,385 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dba3a4486bb1d3b66f2a1866028090dcdcc589aa484bdf6f9c88f29107bd1423

Height

#479,256

Difficulty

10.503872

Transactions

1

Size

799 B

Version

2

Bits

0a80fdc8

Nonce

65,804

Timestamp

4/7/2014, 2:02:32 PM

Confirmations

6,346,385

Merkle Root

7c52a3f8a605fb6b7798417144bb4d68386e8fda59f7f6fc62154c75d6d8b740
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.

3.958 × 10⁹³(94-digit number)
39585004076833132661…86894211317715746399
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
3.958 × 10⁹³(94-digit number)
39585004076833132661…86894211317715746399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.917 × 10⁹³(94-digit number)
79170008153666265323…73788422635431492799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.583 × 10⁹⁴(95-digit number)
15834001630733253064…47576845270862985599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.166 × 10⁹⁴(95-digit number)
31668003261466506129…95153690541725971199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
6.333 × 10⁹⁴(95-digit number)
63336006522933012258…90307381083451942399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.266 × 10⁹⁵(96-digit number)
12667201304586602451…80614762166903884799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.533 × 10⁹⁵(96-digit number)
25334402609173204903…61229524333807769599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.066 × 10⁹⁵(96-digit number)
50668805218346409807…22459048667615539199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.013 × 10⁹⁶(97-digit number)
10133761043669281961…44918097335231078399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.026 × 10⁹⁶(97-digit number)
20267522087338563922…89836194670462156799
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:57,849,232 XPM·at block #6,825,640 · updates every 60s
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