Block #1,382,606

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/24/2015, 7:11:20 AM · Difficulty 10.8090 · 5,457,521 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dc62fa1b549ce985b2e681d32b1c3b21046d3a20ce7269a312d067bf6f6d232d

Height

#1,382,606

Difficulty

10.808956

Transactions

3

Size

2.37 KB

Version

2

Bits

0acf17be

Nonce

250,123,470

Timestamp

12/24/2015, 7:11:20 AM

Confirmations

5,457,521

Merkle Root

95b74e17f5ca77ebd6f5ea3ae6c1b1b7c3053976225fd5e89076dac79b16ca3e
Transactions (3)
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.

1.534 × 10⁹⁵(96-digit number)
15342598006539058388…97297821916676732799
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
1.534 × 10⁹⁵(96-digit number)
15342598006539058388…97297821916676732799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.068 × 10⁹⁵(96-digit number)
30685196013078116776…94595643833353465599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.137 × 10⁹⁵(96-digit number)
61370392026156233552…89191287666706931199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.227 × 10⁹⁶(97-digit number)
12274078405231246710…78382575333413862399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.454 × 10⁹⁶(97-digit number)
24548156810462493421…56765150666827724799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.909 × 10⁹⁶(97-digit number)
49096313620924986842…13530301333655449599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
9.819 × 10⁹⁶(97-digit number)
98192627241849973684…27060602667310899199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.963 × 10⁹⁷(98-digit number)
19638525448369994736…54121205334621798399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.927 × 10⁹⁷(98-digit number)
39277050896739989473…08242410669243596799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
7.855 × 10⁹⁷(98-digit number)
78554101793479978947…16484821338487193599
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:57,965,330 XPM·at block #6,840,126 · updates every 60s
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