Block #63,444

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/19/2013, 1:30:35 AM · Difficulty 8.9792 · 6,753,687 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8079608a5927b338a07f4de4683d473fe40b52d395c67d029d7695b3a253f35e

Height

#63,444

Difficulty

8.979185

Transactions

1

Size

202 B

Version

2

Bits

08faabe2

Nonce

1,212

Timestamp

7/19/2013, 1:30:35 AM

Confirmations

6,753,687

Merkle Root

c021f117b569e7b1abd2aa95a51ff3f43a75f183ee58a9ba4df2a839e987d963
Transactions (1)
1 in → 1 out12.3900 XPM110 B
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.

1.510 × 10⁹⁹(100-digit number)
15100767082148730395…61024667954639143751
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
1.510 × 10⁹⁹(100-digit number)
15100767082148730395…61024667954639143751
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.020 × 10⁹⁹(100-digit number)
30201534164297460790…22049335909278287501
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
6.040 × 10⁹⁹(100-digit number)
60403068328594921580…44098671818556575001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.208 × 10¹⁰⁰(101-digit number)
12080613665718984316…88197343637113150001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.416 × 10¹⁰⁰(101-digit number)
24161227331437968632…76394687274226300001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.832 × 10¹⁰⁰(101-digit number)
48322454662875937264…52789374548452600001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
9.664 × 10¹⁰⁰(101-digit number)
96644909325751874529…05578749096905200001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.932 × 10¹⁰¹(102-digit number)
19328981865150374905…11157498193810400001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.865 × 10¹⁰¹(102-digit number)
38657963730300749811…22314996387620800001
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,781,082 XPM·at block #6,817,130 · updates every 60s
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