Block #1,497,056

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/15/2016, 12:05:33 AM · Difficulty 10.6455 · 5,328,501 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f4a3622ea9e5afc81c1f1d33387d323e415107833de0d622fe2a23ccec559b1a

Height

#1,497,056

Difficulty

10.645496

Transactions

2

Size

1.21 KB

Version

2

Bits

0aa53f38

Nonce

74,990,014

Timestamp

3/15/2016, 12:05:33 AM

Confirmations

5,328,501

Merkle Root

7a18e8d49eb12ad72990530f447260b30ac7ad49f9e910309f5fe54ed4454f51
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.

1.489 × 10⁹⁵(96-digit number)
14892399873795717964…03558332182096696321
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
1.489 × 10⁹⁵(96-digit number)
14892399873795717964…03558332182096696321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.978 × 10⁹⁵(96-digit number)
29784799747591435929…07116664364193392641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.956 × 10⁹⁵(96-digit number)
59569599495182871859…14233328728386785281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.191 × 10⁹⁶(97-digit number)
11913919899036574371…28466657456773570561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.382 × 10⁹⁶(97-digit number)
23827839798073148743…56933314913547141121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.765 × 10⁹⁶(97-digit number)
47655679596146297487…13866629827094282241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
9.531 × 10⁹⁶(97-digit number)
95311359192292594975…27733259654188564481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.906 × 10⁹⁷(98-digit number)
19062271838458518995…55466519308377128961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.812 × 10⁹⁷(98-digit number)
38124543676917037990…10933038616754257921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.624 × 10⁹⁷(98-digit number)
76249087353834075980…21866077233508515841
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:57,848,556 XPM·at block #6,825,556 · updates every 60s
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