Block #1,370,400

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/15/2015, 3:11:22 PM · Difficulty 10.8186 · 5,443,496 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4f69827adea1b4ffbd66a68f7efb88b52f80e44fba728747e0103ea7df22c7c5

Height

#1,370,400

Difficulty

10.818634

Transactions

2

Size

833 B

Version

2

Bits

0ad191fd

Nonce

733,544,898

Timestamp

12/15/2015, 3:11:22 PM

Confirmations

5,443,496

Merkle Root

be5df1e4ed9a30cdd7a49e304836fe168aeb1d5043dc17e5fd5a67e6cec09051
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.

1.427 × 10⁹⁷(98-digit number)
14273758096256260418…52816910457459558401
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
1.427 × 10⁹⁷(98-digit number)
14273758096256260418…52816910457459558401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.854 × 10⁹⁷(98-digit number)
28547516192512520837…05633820914919116801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.709 × 10⁹⁷(98-digit number)
57095032385025041675…11267641829838233601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.141 × 10⁹⁸(99-digit number)
11419006477005008335…22535283659676467201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.283 × 10⁹⁸(99-digit number)
22838012954010016670…45070567319352934401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.567 × 10⁹⁸(99-digit number)
45676025908020033340…90141134638705868801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
9.135 × 10⁹⁸(99-digit number)
91352051816040066680…80282269277411737601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.827 × 10⁹⁹(100-digit number)
18270410363208013336…60564538554823475201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.654 × 10⁹⁹(100-digit number)
36540820726416026672…21129077109646950401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.308 × 10⁹⁹(100-digit number)
73081641452832053344…42258154219293900801
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:57,755,245 XPM·at block #6,813,895 · updates every 60s
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