Block #1,383,445

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/24/2015, 9:07:31 PM · Difficulty 10.8090 · 5,442,112 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1351337449c8a180692c97b7ba58020b3e253c012ecc84241f49e40b318a17cc

Height

#1,383,445

Difficulty

10.809025

Transactions

2

Size

1.05 KB

Version

2

Bits

0acf1c4a

Nonce

332,694,171

Timestamp

12/24/2015, 9:07:31 PM

Confirmations

5,442,112

Merkle Root

f94db102dd6ec8d8644c29d746bf921b553746ca02d3dbb6abfa3687d748e22c
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.

2.978 × 10⁹⁴(95-digit number)
29780157518545298886…63612244392254931839
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
2.978 × 10⁹⁴(95-digit number)
29780157518545298886…63612244392254931839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
5.956 × 10⁹⁴(95-digit number)
59560315037090597773…27224488784509863679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.191 × 10⁹⁵(96-digit number)
11912063007418119554…54448977569019727359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.382 × 10⁹⁵(96-digit number)
23824126014836239109…08897955138039454719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.764 × 10⁹⁵(96-digit number)
47648252029672478219…17795910276078909439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
9.529 × 10⁹⁵(96-digit number)
95296504059344956438…35591820552157818879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.905 × 10⁹⁶(97-digit number)
19059300811868991287…71183641104315637759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.811 × 10⁹⁶(97-digit number)
38118601623737982575…42367282208631275519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
7.623 × 10⁹⁶(97-digit number)
76237203247475965150…84734564417262551039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.524 × 10⁹⁷(98-digit number)
15247440649495193030…69469128834525102079
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 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
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 1CC formula:

1CC: 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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