Block #496,937

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/17/2014, 8:26:40 AM · Difficulty 10.7608 · 6,327,561 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2ef20f304251264c4592b2d8c5a2f9f5209f61b40b3c7dba039e86b094db40e6

Height

#496,937

Difficulty

10.760808

Transactions

2

Size

433 B

Version

2

Bits

0ac2c448

Nonce

169,164,183

Timestamp

4/17/2014, 8:26:40 AM

Confirmations

6,327,561

Merkle Root

eed067a69ff13bbb6cb6c38919a4675b2d0a385b8973212632c2c5b56d6f9bdf
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.

7.172 × 10⁹⁷(98-digit number)
71724126363183743890…38168285963904119041
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
7.172 × 10⁹⁷(98-digit number)
71724126363183743890…38168285963904119041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.434 × 10⁹⁸(99-digit number)
14344825272636748778…76336571927808238081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.868 × 10⁹⁸(99-digit number)
28689650545273497556…52673143855616476161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.737 × 10⁹⁸(99-digit number)
57379301090546995112…05346287711232952321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.147 × 10⁹⁹(100-digit number)
11475860218109399022…10692575422465904641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.295 × 10⁹⁹(100-digit number)
22951720436218798044…21385150844931809281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.590 × 10⁹⁹(100-digit number)
45903440872437596089…42770301689863618561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.180 × 10⁹⁹(100-digit number)
91806881744875192179…85540603379727237121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.836 × 10¹⁰⁰(101-digit number)
18361376348975038435…71081206759454474241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.672 × 10¹⁰⁰(101-digit number)
36722752697950076871…42162413518908948481
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:57,840,057 XPM·at block #6,824,497 · updates every 60s
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