Block #2,001,879

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 2/27/2017, 5:34:04 PM · Difficulty 10.7405 · 4,841,555 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7c1bc589aea5154f78a426a94c13e8195af16686b690641d51f97a90f75be92d

Height

#2,001,879

Difficulty

10.740476

Transactions

2

Size

2.01 KB

Version

2

Bits

0abd8fd3

Nonce

273,479,763

Timestamp

2/27/2017, 5:34:04 PM

Confirmations

4,841,555

Merkle Root

d8b7c98f1ccf8a05367ce4a75a751b3b49ad0d64db88e52593448a12665d578d
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.

1.220 × 10⁹⁷(98-digit number)
12205673068214705996…03774493578801233921
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
1.220 × 10⁹⁷(98-digit number)
12205673068214705996…03774493578801233921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.441 × 10⁹⁷(98-digit number)
24411346136429411993…07548987157602467841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.882 × 10⁹⁷(98-digit number)
48822692272858823987…15097974315204935681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.764 × 10⁹⁷(98-digit number)
97645384545717647975…30195948630409871361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.952 × 10⁹⁸(99-digit number)
19529076909143529595…60391897260819742721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.905 × 10⁹⁸(99-digit number)
39058153818287059190…20783794521639485441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.811 × 10⁹⁸(99-digit number)
78116307636574118380…41567589043278970881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.562 × 10⁹⁹(100-digit number)
15623261527314823676…83135178086557941761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.124 × 10⁹⁹(100-digit number)
31246523054629647352…66270356173115883521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.249 × 10⁹⁹(100-digit number)
62493046109259294704…32540712346231767041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.249 × 10¹⁰⁰(101-digit number)
12498609221851858940…65081424692463534081
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:57,991,843 XPM·at block #6,843,433 · updates every 60s
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