Block #96,696

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/4/2013, 8:18:39 AM · Difficulty 9.2774 · 6,712,675 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b758097a54f94a68afb39d28aa6fbbe63a1bcf52d470eedd32d5b6c3c999dedd

Height

#96,696

Difficulty

9.277415

Transactions

4

Size

1.01 KB

Version

2

Bits

094704a7

Nonce

62,631

Timestamp

8/4/2013, 8:18:39 AM

Confirmations

6,712,675

Merkle Root

a3404e4220e1840075f1848ba48f1d296eeb096c8910c642974b14d7c3956033
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.

3.617 × 10¹⁰¹(102-digit number)
36177401103545848039…10781226851844736199
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
3.617 × 10¹⁰¹(102-digit number)
36177401103545848039…10781226851844736199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.235 × 10¹⁰¹(102-digit number)
72354802207091696079…21562453703689472399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.447 × 10¹⁰²(103-digit number)
14470960441418339215…43124907407378944799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.894 × 10¹⁰²(103-digit number)
28941920882836678431…86249814814757889599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.788 × 10¹⁰²(103-digit number)
57883841765673356863…72499629629515779199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.157 × 10¹⁰³(104-digit number)
11576768353134671372…44999259259031558399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.315 × 10¹⁰³(104-digit number)
23153536706269342745…89998518518063116799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.630 × 10¹⁰³(104-digit number)
46307073412538685490…79997037036126233599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
9.261 × 10¹⁰³(104-digit number)
92614146825077370981…59994074072252467199
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:57,719,037 XPM·at block #6,809,370 · updates every 60s
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