Block #1,479,282

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/1/2016, 10:05:08 PM · Difficulty 10.7124 · 5,354,443 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
67dedf76616e82fe80cbc31708e597ecaa4650b01ae17da3a4da3d877332c6ad

Height

#1,479,282

Difficulty

10.712380

Transactions

2

Size

1.25 KB

Version

2

Bits

0ab65e87

Nonce

615,772,963

Timestamp

3/1/2016, 10:05:08 PM

Confirmations

5,354,443

Merkle Root

d6f8384fc90a1ebb1cd90ec8983beedd4d3665e993053d00672e5a8b80d65127
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.

2.426 × 10⁹⁷(98-digit number)
24264764358663408622…00033864598152020479
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
2.426 × 10⁹⁷(98-digit number)
24264764358663408622…00033864598152020479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.852 × 10⁹⁷(98-digit number)
48529528717326817244…00067729196304040959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
9.705 × 10⁹⁷(98-digit number)
97059057434653634489…00135458392608081919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.941 × 10⁹⁸(99-digit number)
19411811486930726897…00270916785216163839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.882 × 10⁹⁸(99-digit number)
38823622973861453795…00541833570432327679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.764 × 10⁹⁸(99-digit number)
77647245947722907591…01083667140864655359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.552 × 10⁹⁹(100-digit number)
15529449189544581518…02167334281729310719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.105 × 10⁹⁹(100-digit number)
31058898379089163036…04334668563458621439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
6.211 × 10⁹⁹(100-digit number)
62117796758178326072…08669337126917242879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.242 × 10¹⁰⁰(101-digit number)
12423559351635665214…17338674253834485759
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:57,914,022 XPM·at block #6,833,724 · updates every 60s
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