Block #485,356

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/11/2014, 12:30:13 AM · Difficulty 10.6072 · 6,313,025 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
55ec4af4046f7fb8e000b56f8f34506ece122c08c65f4c1b45d11f280e6eda6a

Height

#485,356

Difficulty

10.607249

Transactions

2

Size

52.02 KB

Version

2

Bits

0a9b74ab

Nonce

142,047,439

Timestamp

4/11/2014, 12:30:13 AM

Confirmations

6,313,025

Merkle Root

0aae0ee75d5e2c6ad2f3ddc49f39d52f070ee4cc48c36d95400f2b8c197cb295
Transactions (2)
1 in → 1 out9.4100 XPM112 B
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.

8.884 × 10⁹⁸(99-digit number)
88842748772047008557…20472371848219832319
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
8.884 × 10⁹⁸(99-digit number)
88842748772047008557…20472371848219832319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.776 × 10⁹⁹(100-digit number)
17768549754409401711…40944743696439664639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.553 × 10⁹⁹(100-digit number)
35537099508818803423…81889487392879329279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.107 × 10⁹⁹(100-digit number)
71074199017637606846…63778974785758658559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.421 × 10¹⁰⁰(101-digit number)
14214839803527521369…27557949571517317119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.842 × 10¹⁰⁰(101-digit number)
28429679607055042738…55115899143034634239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.685 × 10¹⁰⁰(101-digit number)
56859359214110085476…10231798286069268479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.137 × 10¹⁰¹(102-digit number)
11371871842822017095…20463596572138536959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.274 × 10¹⁰¹(102-digit number)
22743743685644034190…40927193144277073919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.548 × 10¹⁰¹(102-digit number)
45487487371288068381…81854386288554147839
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:57,631,054 XPM·at block #6,798,380 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.