Block #1,475,263

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/28/2016, 9:05:29 AM · Difficulty 10.6910 · 5,340,866 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
90d5f7166989e8ce567df779d2711c6f859bb9e244ada394e65147a1cdf6982a

Height

#1,475,263

Difficulty

10.690987

Transactions

2

Size

1.68 KB

Version

2

Bits

0ab0e482

Nonce

1,206,441,712

Timestamp

2/28/2016, 9:05:29 AM

Confirmations

5,340,866

Merkle Root

fdf91e41e7a1ebc9f3334a97b91d71ea01189f578f5904851e9b03b74d288d5a
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.

1.805 × 10⁹⁶(97-digit number)
18054800301001528568…56659321131015920641
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
1.805 × 10⁹⁶(97-digit number)
18054800301001528568…56659321131015920641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.610 × 10⁹⁶(97-digit number)
36109600602003057137…13318642262031841281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.221 × 10⁹⁶(97-digit number)
72219201204006114274…26637284524063682561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.444 × 10⁹⁷(98-digit number)
14443840240801222854…53274569048127365121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.888 × 10⁹⁷(98-digit number)
28887680481602445709…06549138096254730241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.777 × 10⁹⁷(98-digit number)
57775360963204891419…13098276192509460481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.155 × 10⁹⁸(99-digit number)
11555072192640978283…26196552385018920961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.311 × 10⁹⁸(99-digit number)
23110144385281956567…52393104770037841921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.622 × 10⁹⁸(99-digit number)
46220288770563913135…04786209540075683841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.244 × 10⁹⁸(99-digit number)
92440577541127826271…09572419080151367681
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:57,773,157 XPM·at block #6,816,128 · updates every 60s
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