Block #1,512,744

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 3/26/2016, 6:55:41 AM · Difficulty 10.6043 · 5,302,126 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1391251a9b4e190567fc09f558adb61e56f77fbcad0f8e07f0bf5d0b30e82940

Height

#1,512,744

Difficulty

10.604324

Transactions

4

Size

5.84 KB

Version

2

Bits

0a9ab4ff

Nonce

169,483,921

Timestamp

3/26/2016, 6:55:41 AM

Confirmations

5,302,126

Merkle Root

f31d27c4b6bb13bbf96202baf89469f65b64d65c37d7488b02f81fc0503a5db4
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.

2.443 × 10⁹⁴(95-digit number)
24434977476694080425…26104743506156020899
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
2.443 × 10⁹⁴(95-digit number)
24434977476694080425…26104743506156020899
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.886 × 10⁹⁴(95-digit number)
48869954953388160850…52209487012312041799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
9.773 × 10⁹⁴(95-digit number)
97739909906776321700…04418974024624083599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.954 × 10⁹⁵(96-digit number)
19547981981355264340…08837948049248167199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.909 × 10⁹⁵(96-digit number)
39095963962710528680…17675896098496334399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.819 × 10⁹⁵(96-digit number)
78191927925421057360…35351792196992668799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.563 × 10⁹⁶(97-digit number)
15638385585084211472…70703584393985337599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.127 × 10⁹⁶(97-digit number)
31276771170168422944…41407168787970675199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
6.255 × 10⁹⁶(97-digit number)
62553542340336845888…82814337575941350399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.251 × 10⁹⁷(98-digit number)
12510708468067369177…65628675151882700799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
2.502 × 10⁹⁷(98-digit number)
25021416936134738355…31257350303765401599
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the First 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,763,046 XPM·at block #6,814,869 · updates every 60s
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