Block #373,802

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/24/2014, 1:45:41 PM · Difficulty 10.4249 · 6,437,197 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
96fd88daa1c3dfa59cdbd21528a5385c90829d97964ef5ac3401978ed5d5067e

Height

#373,802

Difficulty

10.424906

Transactions

2

Size

1.23 KB

Version

2

Bits

0a6cc6a8

Nonce

192,255

Timestamp

1/24/2014, 1:45:41 PM

Confirmations

6,437,197

Merkle Root

d2d8849d095f6778ce48583457e44f3807470fff3a8f69093ddf2f1056d04a6b
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.

6.450 × 10⁹⁷(98-digit number)
64504338222731134265…83619153014440013969
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
6.450 × 10⁹⁷(98-digit number)
64504338222731134265…83619153014440013969
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.290 × 10⁹⁸(99-digit number)
12900867644546226853…67238306028880027939
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.580 × 10⁹⁸(99-digit number)
25801735289092453706…34476612057760055879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.160 × 10⁹⁸(99-digit number)
51603470578184907412…68953224115520111759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.032 × 10⁹⁹(100-digit number)
10320694115636981482…37906448231040223519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.064 × 10⁹⁹(100-digit number)
20641388231273962965…75812896462080447039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.128 × 10⁹⁹(100-digit number)
41282776462547925930…51625792924160894079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
8.256 × 10⁹⁹(100-digit number)
82565552925095851860…03251585848321788159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.651 × 10¹⁰⁰(101-digit number)
16513110585019170372…06503171696643576319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.302 × 10¹⁰⁰(101-digit number)
33026221170038340744…13006343393287152639
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:57,732,095 XPM·at block #6,810,998 · updates every 60s
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