Block #1,499,274

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/16/2016, 1:06:37 PM · Difficulty 10.6453 · 5,327,377 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ce7d72444918b2704e4d73fcfc7a736ceea42b94039cbad6854e1aa4006112d5

Height

#1,499,274

Difficulty

10.645337

Transactions

2

Size

1.14 KB

Version

2

Bits

0aa534d0

Nonce

866,653,606

Timestamp

3/16/2016, 1:06:37 PM

Confirmations

5,327,377

Merkle Root

a3e15a302976bd42bacf7ccda7fc72b9c7100d789a4c363bc6cee94c6e0ddc20
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.

2.397 × 10⁹⁵(96-digit number)
23972986648875750607…42536130057909772801
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
2.397 × 10⁹⁵(96-digit number)
23972986648875750607…42536130057909772801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.794 × 10⁹⁵(96-digit number)
47945973297751501215…85072260115819545601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.589 × 10⁹⁵(96-digit number)
95891946595503002431…70144520231639091201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.917 × 10⁹⁶(97-digit number)
19178389319100600486…40289040463278182401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.835 × 10⁹⁶(97-digit number)
38356778638201200972…80578080926556364801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.671 × 10⁹⁶(97-digit number)
76713557276402401945…61156161853112729601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.534 × 10⁹⁷(98-digit number)
15342711455280480389…22312323706225459201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.068 × 10⁹⁷(98-digit number)
30685422910560960778…44624647412450918401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.137 × 10⁹⁷(98-digit number)
61370845821121921556…89249294824901836801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.227 × 10⁹⁸(99-digit number)
12274169164224384311…78498589649803673601
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:57,857,357 XPM·at block #6,826,650 · updates every 60s
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