Block #371,703

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/23/2014, 2:10:46 AM · Difficulty 10.4291 · 6,429,126 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7071ac4522fa6d6477c5ad782e352bfcd67665d20a2ff1c42cc410e643bca89d

Height

#371,703

Difficulty

10.429099

Transactions

5

Size

1.63 KB

Version

2

Bits

0a6dd973

Nonce

10,791

Timestamp

1/23/2014, 2:10:46 AM

Confirmations

6,429,126

Merkle Root

7993b38daa763b3e07b3f670f29685fd07306d771bac6a291a0d59f04391494a
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.

2.145 × 10⁹⁹(100-digit number)
21454666154341975264…32088007902053176319
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
2.145 × 10⁹⁹(100-digit number)
21454666154341975264…32088007902053176319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.290 × 10⁹⁹(100-digit number)
42909332308683950528…64176015804106352639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
8.581 × 10⁹⁹(100-digit number)
85818664617367901057…28352031608212705279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.716 × 10¹⁰⁰(101-digit number)
17163732923473580211…56704063216425410559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.432 × 10¹⁰⁰(101-digit number)
34327465846947160423…13408126432850821119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.865 × 10¹⁰⁰(101-digit number)
68654931693894320846…26816252865701642239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.373 × 10¹⁰¹(102-digit number)
13730986338778864169…53632505731403284479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.746 × 10¹⁰¹(102-digit number)
27461972677557728338…07265011462806568959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.492 × 10¹⁰¹(102-digit number)
54923945355115456676…14530022925613137919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.098 × 10¹⁰²(103-digit number)
10984789071023091335…29060045851226275839
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:57,650,689 XPM·at block #6,800,828 · updates every 60s
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