Block #982,173

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 3/20/2015, 2:02:26 AM · Difficulty 10.8485 · 5,825,959 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6ecf914bf7895b71eacdb916541aa26919f3be87a3e1a6fc971d10b9937a586d

Height

#982,173

Difficulty

10.848455

Transactions

3

Size

4.33 KB

Version

2

Bits

0ad9345d

Nonce

1,453,197,341

Timestamp

3/20/2015, 2:02:26 AM

Confirmations

5,825,959

Merkle Root

5a606140a5e07f98e7a12687253b6891adeb364c9eea17defc534db3d8680c11
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.

2.910 × 10⁹⁷(98-digit number)
29104379544081434940…37818685053181917441
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
2.910 × 10⁹⁷(98-digit number)
29104379544081434940…37818685053181917441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.820 × 10⁹⁷(98-digit number)
58208759088162869881…75637370106363834881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.164 × 10⁹⁸(99-digit number)
11641751817632573976…51274740212727669761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.328 × 10⁹⁸(99-digit number)
23283503635265147952…02549480425455339521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.656 × 10⁹⁸(99-digit number)
46567007270530295905…05098960850910679041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.313 × 10⁹⁸(99-digit number)
93134014541060591810…10197921701821358081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.862 × 10⁹⁹(100-digit number)
18626802908212118362…20395843403642716161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.725 × 10⁹⁹(100-digit number)
37253605816424236724…40791686807285432321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.450 × 10⁹⁹(100-digit number)
74507211632848473448…81583373614570864641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.490 × 10¹⁰⁰(101-digit number)
14901442326569694689…63166747229141729281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.980 × 10¹⁰⁰(101-digit number)
29802884653139389379…26333494458283458561
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the Second 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,709,097 XPM·at block #6,808,131 · updates every 60s
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