Block #390,091

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/4/2014, 10:09:23 PM · Difficulty 10.4250 · 6,435,568 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
261e41a594c14bf533ec2f6cd0f7b2acd18c1ab237d77dd1c8e0e110cebea471

Height

#390,091

Difficulty

10.424970

Transactions

1

Size

800 B

Version

2

Bits

0a6ccad2

Nonce

73,025

Timestamp

2/4/2014, 10:09:23 PM

Confirmations

6,435,568

Merkle Root

e8195a0e7c7556f74154a9244b91fb9c79fbaad6abff98cafb3973cdaa723906
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.

3.190 × 10⁹⁷(98-digit number)
31900786834707776317…48693715480018943999
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
3.190 × 10⁹⁷(98-digit number)
31900786834707776317…48693715480018943999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
6.380 × 10⁹⁷(98-digit number)
63801573669415552634…97387430960037887999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.276 × 10⁹⁸(99-digit number)
12760314733883110526…94774861920075775999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.552 × 10⁹⁸(99-digit number)
25520629467766221053…89549723840151551999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.104 × 10⁹⁸(99-digit number)
51041258935532442107…79099447680303103999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.020 × 10⁹⁹(100-digit number)
10208251787106488421…58198895360606207999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.041 × 10⁹⁹(100-digit number)
20416503574212976843…16397790721212415999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.083 × 10⁹⁹(100-digit number)
40833007148425953686…32795581442424831999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
8.166 × 10⁹⁹(100-digit number)
81666014296851907372…65591162884849663999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.633 × 10¹⁰⁰(101-digit number)
16333202859370381474…31182325769699327999
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:57,849,379 XPM·at block #6,825,658 · updates every 60s
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