Block #396,466

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 2/9/2014, 10:28:22 AM · Difficulty 10.4123 · 6,407,546 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cd5aad30ce01c928526a66aa35af7eea574c40fc8514c1442c89f91a2e0f16af

Height

#396,466

Difficulty

10.412272

Transactions

1

Size

835 B

Version

2

Bits

0a698aa1

Nonce

4,874

Timestamp

2/9/2014, 10:28:22 AM

Confirmations

6,407,546

Merkle Root

fa3f2c82cc4e17d97e6a22ff3e16d3e64a8006ba64932ded66c1a5e50a3de09b
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.

1.228 × 10¹⁰⁰(101-digit number)
12289123690489730200…03594526604123783679
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
1.228 × 10¹⁰⁰(101-digit number)
12289123690489730200…03594526604123783679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.457 × 10¹⁰⁰(101-digit number)
24578247380979460401…07189053208247567359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.915 × 10¹⁰⁰(101-digit number)
49156494761958920802…14378106416495134719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
9.831 × 10¹⁰⁰(101-digit number)
98312989523917841605…28756212832990269439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.966 × 10¹⁰¹(102-digit number)
19662597904783568321…57512425665980538879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.932 × 10¹⁰¹(102-digit number)
39325195809567136642…15024851331961077759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
7.865 × 10¹⁰¹(102-digit number)
78650391619134273284…30049702663922155519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.573 × 10¹⁰²(103-digit number)
15730078323826854656…60099405327844311039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.146 × 10¹⁰²(103-digit number)
31460156647653709313…20198810655688622079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
6.292 × 10¹⁰²(103-digit number)
62920313295307418627…40397621311377244159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.258 × 10¹⁰³(104-digit number)
12584062659061483725…80795242622754488319
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,676,144 XPM·at block #6,804,011 · 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.