Block #1,255,763

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/27/2015, 6:02:38 AM · Difficulty 10.8015 · 5,562,010 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
05a4529be829ab29f36943cbfa0c06d3f126ea259eb35adc414ee661859657f2

Height

#1,255,763

Difficulty

10.801500

Transactions

2

Size

806 B

Version

2

Bits

0acd2f1a

Nonce

1,666,274,626

Timestamp

9/27/2015, 6:02:38 AM

Confirmations

5,562,010

Merkle Root

b789bd81951ec3a0c0a6f9be4454f5aff9a9f847768b3c8f8ca2ae82301d80f4
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.

1.401 × 10⁹⁶(97-digit number)
14010144236477709343…89844037998165919041
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
1.401 × 10⁹⁶(97-digit number)
14010144236477709343…89844037998165919041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.802 × 10⁹⁶(97-digit number)
28020288472955418687…79688075996331838081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.604 × 10⁹⁶(97-digit number)
56040576945910837375…59376151992663676161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.120 × 10⁹⁷(98-digit number)
11208115389182167475…18752303985327352321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.241 × 10⁹⁷(98-digit number)
22416230778364334950…37504607970654704641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.483 × 10⁹⁷(98-digit number)
44832461556728669900…75009215941309409281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.966 × 10⁹⁷(98-digit number)
89664923113457339801…50018431882618818561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.793 × 10⁹⁸(99-digit number)
17932984622691467960…00036863765237637121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.586 × 10⁹⁸(99-digit number)
35865969245382935920…00073727530475274241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.173 × 10⁹⁸(99-digit number)
71731938490765871840…00147455060950548481
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:57,786,241 XPM·at block #6,817,772 · updates every 60s
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