Block #824,888

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 11/23/2014, 8:57:20 PM · Difficulty 10.9772 · 6,002,222 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4288bcae6976a91b66994c405b6a38acbc4ffe27e1c8942198fca63da4de44f6

Height

#824,888

Difficulty

10.977160

Transactions

2

Size

724 B

Version

2

Bits

0afa2730

Nonce

195,923,682

Timestamp

11/23/2014, 8:57:20 PM

Confirmations

6,002,222

Merkle Root

82d3d5360778f3d259af0fe644b69df0b9f140048bcef0a85b3ae841de1be963
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.

5.415 × 10⁹⁶(97-digit number)
54157227656860479331…93155430185876531201
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
5.415 × 10⁹⁶(97-digit number)
54157227656860479331…93155430185876531201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.083 × 10⁹⁷(98-digit number)
10831445531372095866…86310860371753062401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.166 × 10⁹⁷(98-digit number)
21662891062744191732…72621720743506124801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.332 × 10⁹⁷(98-digit number)
43325782125488383465…45243441487012249601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.665 × 10⁹⁷(98-digit number)
86651564250976766931…90486882974024499201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.733 × 10⁹⁸(99-digit number)
17330312850195353386…80973765948048998401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.466 × 10⁹⁸(99-digit number)
34660625700390706772…61947531896097996801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.932 × 10⁹⁸(99-digit number)
69321251400781413544…23895063792195993601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.386 × 10⁹⁹(100-digit number)
13864250280156282708…47790127584391987201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.772 × 10⁹⁹(100-digit number)
27728500560312565417…95580255168783974401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
5.545 × 10⁹⁹(100-digit number)
55457001120625130835…91160510337567948801
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:57,861,059 XPM·at block #6,827,109 · updates every 60s
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