Block #496,924

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/17/2014, 8:16:19 AM · Difficulty 10.7607 · 6,330,070 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2998dbb0d9c7c3ebe5c9654379715fa057aed18643aa12a7fe40c1ad0f46067c

Height

#496,924

Difficulty

10.760725

Transactions

3

Size

1.31 KB

Version

2

Bits

0ac2bedd

Nonce

21,250,040

Timestamp

4/17/2014, 8:16:19 AM

Confirmations

6,330,070

Merkle Root

1a6a80ee5062b7d55eb736b8906b52b598d0494b197c65f2ec46d7432b7cbbc2
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.

3.138 × 10⁹⁴(95-digit number)
31382169900638156081…18934949850158799421
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
3.138 × 10⁹⁴(95-digit number)
31382169900638156081…18934949850158799421
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.276 × 10⁹⁴(95-digit number)
62764339801276312163…37869899700317598841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.255 × 10⁹⁵(96-digit number)
12552867960255262432…75739799400635197681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.510 × 10⁹⁵(96-digit number)
25105735920510524865…51479598801270395361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.021 × 10⁹⁵(96-digit number)
50211471841021049730…02959197602540790721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.004 × 10⁹⁶(97-digit number)
10042294368204209946…05918395205081581441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.008 × 10⁹⁶(97-digit number)
20084588736408419892…11836790410163162881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.016 × 10⁹⁶(97-digit number)
40169177472816839784…23673580820326325761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
8.033 × 10⁹⁶(97-digit number)
80338354945633679568…47347161640652651521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.606 × 10⁹⁷(98-digit number)
16067670989126735913…94694323281305303041
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:57,860,127 XPM·at block #6,826,993 · updates every 60s
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