Block #96,541

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/4/2013, 6:19:42 AM · Difficulty 9.2721 · 6,711,378 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4e312184f1f38ac6d17a6cce107d6f1e08176ae868d572878eb87a5213d9cdb7

Height

#96,541

Difficulty

9.272109

Transactions

3

Size

953 B

Version

2

Bits

0945a8ef

Nonce

27,243

Timestamp

8/4/2013, 6:19:42 AM

Confirmations

6,711,378

Merkle Root

f8661c6c2538dd971cb67e0b85086b4e4a9fa45d30f38cd5606f6f200c9f8f42
Transactions (3)
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.

1.865 × 10¹¹⁵(116-digit number)
18659024208443255413…74423748035850122529
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
1.865 × 10¹¹⁵(116-digit number)
18659024208443255413…74423748035850122529
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.731 × 10¹¹⁵(116-digit number)
37318048416886510827…48847496071700245059
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
7.463 × 10¹¹⁵(116-digit number)
74636096833773021655…97694992143400490119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.492 × 10¹¹⁶(117-digit number)
14927219366754604331…95389984286800980239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.985 × 10¹¹⁶(117-digit number)
29854438733509208662…90779968573601960479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.970 × 10¹¹⁶(117-digit number)
59708877467018417324…81559937147203920959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.194 × 10¹¹⁷(118-digit number)
11941775493403683464…63119874294407841919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.388 × 10¹¹⁷(118-digit number)
23883550986807366929…26239748588815683839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.776 × 10¹¹⁷(118-digit number)
47767101973614733859…52479497177631367679
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,707,387 XPM·at block #6,807,918 · updates every 60s
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