Block #119,997

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/16/2013, 8:05:29 PM · Difficulty 9.7525 · 6,707,139 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0a18f1acb931c70cd51a940bb31c995ad2ae4e8af1a47548128cde5ae98d81ff

Height

#119,997

Difficulty

9.752536

Transactions

2

Size

573 B

Version

2

Bits

09c0a62e

Nonce

67,278

Timestamp

8/16/2013, 8:05:29 PM

Confirmations

6,707,139

Merkle Root

1a602ac5b3840de17226520cf01f4f18c96b685e471e7f26c35003ac0754eefa
Transactions (2)
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.

2.292 × 10⁹⁶(97-digit number)
22925645435657012586…04134030021283319519
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
2.292 × 10⁹⁶(97-digit number)
22925645435657012586…04134030021283319519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.585 × 10⁹⁶(97-digit number)
45851290871314025172…08268060042566639039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
9.170 × 10⁹⁶(97-digit number)
91702581742628050345…16536120085133278079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.834 × 10⁹⁷(98-digit number)
18340516348525610069…33072240170266556159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.668 × 10⁹⁷(98-digit number)
36681032697051220138…66144480340533112319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.336 × 10⁹⁷(98-digit number)
73362065394102440276…32288960681066224639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.467 × 10⁹⁸(99-digit number)
14672413078820488055…64577921362132449279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.934 × 10⁹⁸(99-digit number)
29344826157640976110…29155842724264898559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.868 × 10⁹⁸(99-digit number)
58689652315281952221…58311685448529797119
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:57,861,269 XPM·at block #6,827,135 · updates every 60s
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