Block #1,449,439

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/9/2016, 3:05:47 PM · Difficulty 10.7544 · 5,393,458 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5898adaf796ef1b1e24b8f114eb319cdce39eb1462b67a1d90cb2b0f44b42c9c

Height

#1,449,439

Difficulty

10.754385

Transactions

2

Size

1.01 KB

Version

2

Bits

0ac11f61

Nonce

608,822,979

Timestamp

2/9/2016, 3:05:47 PM

Confirmations

5,393,458

Merkle Root

07e420bdcfda3bc4d4b04ac3c7a0f1b980c0ba447874b0bf898e8ecada71721f
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.

8.313 × 10⁹⁵(96-digit number)
83132174244637831291…37754821785571767679
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
8.313 × 10⁹⁵(96-digit number)
83132174244637831291…37754821785571767679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.662 × 10⁹⁶(97-digit number)
16626434848927566258…75509643571143535359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.325 × 10⁹⁶(97-digit number)
33252869697855132516…51019287142287070719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.650 × 10⁹⁶(97-digit number)
66505739395710265033…02038574284574141439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.330 × 10⁹⁷(98-digit number)
13301147879142053006…04077148569148282879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.660 × 10⁹⁷(98-digit number)
26602295758284106013…08154297138296565759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.320 × 10⁹⁷(98-digit number)
53204591516568212026…16308594276593131519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.064 × 10⁹⁸(99-digit number)
10640918303313642405…32617188553186263039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.128 × 10⁹⁸(99-digit number)
21281836606627284810…65234377106372526079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.256 × 10⁹⁸(99-digit number)
42563673213254569621…30468754212745052159
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:57,987,524 XPM·at block #6,842,896 · updates every 60s
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