Block #472,663

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/3/2014, 10:23:35 AM · Difficulty 10.4369 · 6,332,406 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
51805d7b2040e2be63c6ded7e3edefab40a0ee30adbe450be4ee60d22b4804ca

Height

#472,663

Difficulty

10.436865

Transactions

3

Size

808 B

Version

2

Bits

0a6fd66a

Nonce

141,249

Timestamp

4/3/2014, 10:23:35 AM

Confirmations

6,332,406

Merkle Root

34dec6c8f704665abfca0528e7065aef4d22bffcd027861ded54f72422d308d7
Transactions (3)
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.

1.421 × 10⁹⁶(97-digit number)
14214093290923306650…12924697843524024279
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
1.421 × 10⁹⁶(97-digit number)
14214093290923306650…12924697843524024279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.842 × 10⁹⁶(97-digit number)
28428186581846613301…25849395687048048559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.685 × 10⁹⁶(97-digit number)
56856373163693226603…51698791374096097119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.137 × 10⁹⁷(98-digit number)
11371274632738645320…03397582748192194239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.274 × 10⁹⁷(98-digit number)
22742549265477290641…06795165496384388479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.548 × 10⁹⁷(98-digit number)
45485098530954581282…13590330992768776959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
9.097 × 10⁹⁷(98-digit number)
90970197061909162565…27180661985537553919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.819 × 10⁹⁸(99-digit number)
18194039412381832513…54361323971075107839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.638 × 10⁹⁸(99-digit number)
36388078824763665026…08722647942150215679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
7.277 × 10⁹⁸(99-digit number)
72776157649527330052…17445295884300431359
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:57,684,618 XPM·at block #6,805,068 · updates every 60s
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