Block #89,184

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/30/2013, 4:32:09 AM · Difficulty 9.2607 · 6,707,452 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d51296e088bfa2f86b6b2c3d134b560a0574c81fd072308c33623fc104d9502c

Height

#89,184

Difficulty

9.260683

Transactions

3

Size

805 B

Version

2

Bits

0942bc1e

Nonce

212,322

Timestamp

7/30/2013, 4:32:09 AM

Confirmations

6,707,452

Merkle Root

a5606fd131705dcd5f7911eb088e23055ad0b731f57202280096df1e5dc94af4
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.

5.977 × 10¹⁰³(104-digit number)
59779524630831616366…40689510390408913689
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
5.977 × 10¹⁰³(104-digit number)
59779524630831616366…40689510390408913689
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.195 × 10¹⁰⁴(105-digit number)
11955904926166323273…81379020780817827379
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.391 × 10¹⁰⁴(105-digit number)
23911809852332646546…62758041561635654759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.782 × 10¹⁰⁴(105-digit number)
47823619704665293092…25516083123271309519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
9.564 × 10¹⁰⁴(105-digit number)
95647239409330586185…51032166246542619039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.912 × 10¹⁰⁵(106-digit number)
19129447881866117237…02064332493085238079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.825 × 10¹⁰⁵(106-digit number)
38258895763732234474…04128664986170476159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.651 × 10¹⁰⁵(106-digit number)
76517791527464468948…08257329972340952319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.530 × 10¹⁰⁶(107-digit number)
15303558305492893789…16514659944681904639
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:57,617,089 XPM·at block #6,796,635 · updates every 60s
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