Block #945,623

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/21/2015, 6:29:59 AM · Difficulty 10.8984 · 5,870,293 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bb0886f3cc2d482aceae16fb7c229636dec97efa2f32264ae28e47889dfa5772

Height

#945,623

Difficulty

10.898403

Transactions

4

Size

1.03 KB

Version

2

Bits

0ae5fdc2

Nonce

1,227,502,096

Timestamp

2/21/2015, 6:29:59 AM

Confirmations

5,870,293

Merkle Root

dc73c40cdd944f5897869f3e734ac720f11b29ed6c1306babf595ba134c6a2c3
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.

3.591 × 10⁹⁷(98-digit number)
35915275808388326656…56837039073164820479
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
3.591 × 10⁹⁷(98-digit number)
35915275808388326656…56837039073164820479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.183 × 10⁹⁷(98-digit number)
71830551616776653313…13674078146329640959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.436 × 10⁹⁸(99-digit number)
14366110323355330662…27348156292659281919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.873 × 10⁹⁸(99-digit number)
28732220646710661325…54696312585318563839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.746 × 10⁹⁸(99-digit number)
57464441293421322650…09392625170637127679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.149 × 10⁹⁹(100-digit number)
11492888258684264530…18785250341274255359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.298 × 10⁹⁹(100-digit number)
22985776517368529060…37570500682548510719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.597 × 10⁹⁹(100-digit number)
45971553034737058120…75141001365097021439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
9.194 × 10⁹⁹(100-digit number)
91943106069474116241…50282002730194042879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.838 × 10¹⁰⁰(101-digit number)
18388621213894823248…00564005460388085759
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:57,771,438 XPM·at block #6,815,915 · updates every 60s
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