Block #2,004,010

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/1/2017, 8:38:26 AM · Difficulty 10.7297 · 4,810,005 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1e5036ce7ff131f0c4aadeff96916c7a5c05e86499bafd7212be604b34495c5e

Height

#2,004,010

Difficulty

10.729655

Transactions

2

Size

1019 B

Version

2

Bits

0abacaa8

Nonce

569,312,295

Timestamp

3/1/2017, 8:38:26 AM

Confirmations

4,810,005

Merkle Root

76033496d13ef1a41da011fd6e17702b2f275034da733874bd22b198bfed89f1
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.

5.557 × 10⁹⁵(96-digit number)
55577879096579772350…71561271613506785281
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
5.557 × 10⁹⁵(96-digit number)
55577879096579772350…71561271613506785281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.111 × 10⁹⁶(97-digit number)
11115575819315954470…43122543227013570561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.223 × 10⁹⁶(97-digit number)
22231151638631908940…86245086454027141121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.446 × 10⁹⁶(97-digit number)
44462303277263817880…72490172908054282241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.892 × 10⁹⁶(97-digit number)
88924606554527635761…44980345816108564481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.778 × 10⁹⁷(98-digit number)
17784921310905527152…89960691632217128961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.556 × 10⁹⁷(98-digit number)
35569842621811054304…79921383264434257921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.113 × 10⁹⁷(98-digit number)
71139685243622108609…59842766528868515841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.422 × 10⁹⁸(99-digit number)
14227937048724421721…19685533057737031681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.845 × 10⁹⁸(99-digit number)
28455874097448843443…39371066115474063361
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 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
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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,756,204 XPM·at block #6,814,014 · updates every 60s
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