Block #141,490

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/30/2013, 8:40:01 AM · Difficulty 9.8349 · 6,683,461 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e6934aa8d685a766af5cbbd7a79dc8cf3eff192b4ebbee6525f3103bea8d3e2a

Height

#141,490

Difficulty

9.834912

Transactions

2

Size

542 B

Version

2

Bits

09d5bcc9

Nonce

446,426

Timestamp

8/30/2013, 8:40:01 AM

Confirmations

6,683,461

Merkle Root

d2fb221fd8e36c2154b4fe7b0402504fa558afc151a425dab813d3eff2ebc055
Transactions (2)
1 in → 1 out10.3300 XPM109 B
2 in → 1 out500.0900 XPM341 B
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.

9.972 × 10⁹⁹(100-digit number)
99726547475866724555…87421308041372866459
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
9.972 × 10⁹⁹(100-digit number)
99726547475866724555…87421308041372866459
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.994 × 10¹⁰⁰(101-digit number)
19945309495173344911…74842616082745732919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.989 × 10¹⁰⁰(101-digit number)
39890618990346689822…49685232165491465839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.978 × 10¹⁰⁰(101-digit number)
79781237980693379644…99370464330982931679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.595 × 10¹⁰¹(102-digit number)
15956247596138675928…98740928661965863359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.191 × 10¹⁰¹(102-digit number)
31912495192277351857…97481857323931726719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.382 × 10¹⁰¹(102-digit number)
63824990384554703715…94963714647863453439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.276 × 10¹⁰²(103-digit number)
12764998076910940743…89927429295726906879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.552 × 10¹⁰²(103-digit number)
25529996153821881486…79854858591453813759
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:57,843,686 XPM·at block #6,824,950 · updates every 60s
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