Block #466,894

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 3/30/2014, 10:50:09 AM · Difficulty 10.4298 · 6,336,860 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3c98d6b98d9a4318e8c7032b7743e6e44b4fd7b53fd7e7d125a2f01915bc2e75

Height

#466,894

Difficulty

10.429803

Transactions

5

Size

6.28 KB

Version

2

Bits

0a6e078a

Nonce

72,436

Timestamp

3/30/2014, 10:50:09 AM

Confirmations

6,336,860

Merkle Root

201f02e6a4b7dbc35db9f4e1fcd8b43f2b3fd67cf1fa50e027a5bafebf157abe
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.

2.764 × 10⁹⁹(100-digit number)
27647927368628622476…12133687460517765121
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
2.764 × 10⁹⁹(100-digit number)
27647927368628622476…12133687460517765121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.529 × 10⁹⁹(100-digit number)
55295854737257244952…24267374921035530241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.105 × 10¹⁰⁰(101-digit number)
11059170947451448990…48534749842071060481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.211 × 10¹⁰⁰(101-digit number)
22118341894902897981…97069499684142120961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.423 × 10¹⁰⁰(101-digit number)
44236683789805795962…94138999368284241921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
8.847 × 10¹⁰⁰(101-digit number)
88473367579611591924…88277998736568483841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.769 × 10¹⁰¹(102-digit number)
17694673515922318384…76555997473136967681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.538 × 10¹⁰¹(102-digit number)
35389347031844636769…53111994946273935361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.077 × 10¹⁰¹(102-digit number)
70778694063689273539…06223989892547870721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.415 × 10¹⁰²(103-digit number)
14155738812737854707…12447979785095741441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.831 × 10¹⁰²(103-digit number)
28311477625475709415…24895959570191482881
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 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
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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,674,071 XPM·at block #6,803,753 · updates every 60s
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