Block #984,975

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/22/2015, 1:09:39 AM · Difficulty 10.8478 · 5,825,895 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9b6e47812732ed30db1f020da7f5b2bf2defce6b621ac9cb4d787226461247b2

Height

#984,975

Difficulty

10.847820

Transactions

4

Size

1.16 KB

Version

2

Bits

0ad90ac1

Nonce

3,116,518,232

Timestamp

3/22/2015, 1:09:39 AM

Confirmations

5,825,895

Merkle Root

2d884b0a2b768c2425a57673ba13ce6d55c1e037364b9812d5215d6cdd349736
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.

3.351 × 10⁹⁸(99-digit number)
33518307283809365542…24949021830009692159
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
3.351 × 10⁹⁸(99-digit number)
33518307283809365542…24949021830009692159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
6.703 × 10⁹⁸(99-digit number)
67036614567618731085…49898043660019384319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.340 × 10⁹⁹(100-digit number)
13407322913523746217…99796087320038768639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.681 × 10⁹⁹(100-digit number)
26814645827047492434…99592174640077537279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.362 × 10⁹⁹(100-digit number)
53629291654094984868…99184349280155074559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.072 × 10¹⁰⁰(101-digit number)
10725858330818996973…98368698560310149119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.145 × 10¹⁰⁰(101-digit number)
21451716661637993947…96737397120620298239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.290 × 10¹⁰⁰(101-digit number)
42903433323275987894…93474794241240596479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
8.580 × 10¹⁰⁰(101-digit number)
85806866646551975789…86949588482481192959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.716 × 10¹⁰¹(102-digit number)
17161373329310395157…73899176964962385919
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,731,057 XPM·at block #6,810,869 · updates every 60s
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