Block #1,359,140

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/7/2015, 10:33:06 AM · Difficulty 10.8365 · 5,448,438 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
839e1c9704741cb597d6850362bb5e9f4b8d154ed5dd78faf4046af7113bcec1

Height

#1,359,140

Difficulty

10.836485

Transactions

3

Size

5.26 KB

Version

2

Bits

0ad623e6

Nonce

495,066,718

Timestamp

12/7/2015, 10:33:06 AM

Confirmations

5,448,438

Merkle Root

22b1fa43c44e96ca34e57954fa0dbfb99d441b5b03687d2c835e194f74db9b43
Transactions (3)
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.

5.359 × 10⁹³(94-digit number)
53596740322176714959…39150358239588284161
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
5.359 × 10⁹³(94-digit number)
53596740322176714959…39150358239588284161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.071 × 10⁹⁴(95-digit number)
10719348064435342991…78300716479176568321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.143 × 10⁹⁴(95-digit number)
21438696128870685983…56601432958353136641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.287 × 10⁹⁴(95-digit number)
42877392257741371967…13202865916706273281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.575 × 10⁹⁴(95-digit number)
85754784515482743934…26405731833412546561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.715 × 10⁹⁵(96-digit number)
17150956903096548786…52811463666825093121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.430 × 10⁹⁵(96-digit number)
34301913806193097573…05622927333650186241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.860 × 10⁹⁵(96-digit number)
68603827612386195147…11245854667300372481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.372 × 10⁹⁶(97-digit number)
13720765522477239029…22491709334600744961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.744 × 10⁹⁶(97-digit number)
27441531044954478059…44983418669201489921
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:57,704,653 XPM·at block #6,807,577 · updates every 60s
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