Block #1,563,575

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/29/2016, 3:05:25 AM · Difficulty 10.7410 · 5,263,486 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dfe0559a46b9a412f2e265f8e661211c9b0ff498e889437e1c7da670125dbaeb

Height

#1,563,575

Difficulty

10.740961

Transactions

2

Size

901 B

Version

2

Bits

0abdafa7

Nonce

817,519,286

Timestamp

4/29/2016, 3:05:25 AM

Confirmations

5,263,486

Merkle Root

9515df6b981241cda0c11f06b13724c8ebbabe498ba9bbbebc51c019f45ddc1d
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.

7.093 × 10⁹³(94-digit number)
70930309302102275249…68364079314693683001
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
7.093 × 10⁹³(94-digit number)
70930309302102275249…68364079314693683001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.418 × 10⁹⁴(95-digit number)
14186061860420455049…36728158629387366001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.837 × 10⁹⁴(95-digit number)
28372123720840910099…73456317258774732001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.674 × 10⁹⁴(95-digit number)
56744247441681820199…46912634517549464001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.134 × 10⁹⁵(96-digit number)
11348849488336364039…93825269035098928001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.269 × 10⁹⁵(96-digit number)
22697698976672728079…87650538070197856001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.539 × 10⁹⁵(96-digit number)
45395397953345456159…75301076140395712001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.079 × 10⁹⁵(96-digit number)
90790795906690912319…50602152280791424001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.815 × 10⁹⁶(97-digit number)
18158159181338182463…01204304561582848001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.631 × 10⁹⁶(97-digit number)
36316318362676364927…02408609123165696001
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:57,860,671 XPM·at block #6,827,060 · updates every 60s
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