Block #466,469

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/30/2014, 4:58:54 AM · Difficulty 10.4213 · 6,344,280 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9baf2d93385669b336a95506d0eb19cef41ef33365ded259de85414f677c75d6

Height

#466,469

Difficulty

10.421302

Transactions

1

Size

904 B

Version

2

Bits

0a6bda74

Nonce

1,884

Timestamp

3/30/2014, 4:58:54 AM

Confirmations

6,344,280

Merkle Root

1faa28a57147b0a6ef8b4a02559436b06532eaa69ffd49de046ec615fe9a37b7
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.

1.366 × 10¹⁰¹(102-digit number)
13669180049402373195…88583356226989504561
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
1.366 × 10¹⁰¹(102-digit number)
13669180049402373195…88583356226989504561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.733 × 10¹⁰¹(102-digit number)
27338360098804746391…77166712453979009121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.467 × 10¹⁰¹(102-digit number)
54676720197609492782…54333424907958018241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.093 × 10¹⁰²(103-digit number)
10935344039521898556…08666849815916036481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.187 × 10¹⁰²(103-digit number)
21870688079043797112…17333699631832072961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.374 × 10¹⁰²(103-digit number)
43741376158087594225…34667399263664145921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.748 × 10¹⁰²(103-digit number)
87482752316175188451…69334798527328291841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.749 × 10¹⁰³(104-digit number)
17496550463235037690…38669597054656583681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.499 × 10¹⁰³(104-digit number)
34993100926470075380…77339194109313167361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.998 × 10¹⁰³(104-digit number)
69986201852940150761…54678388218626334721
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,730,084 XPM·at block #6,810,748 · updates every 60s
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