Block #469,269

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/1/2014, 2:52:04 AM · Difficulty 10.4279 · 6,339,388 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7a9312bb977a0fb299253dcf624ab60d2bf914538640cdd7165fac7c87d7fdfa

Height

#469,269

Difficulty

10.427940

Transactions

9

Size

4.83 KB

Version

2

Bits

0a6d8d75

Nonce

184,554,640

Timestamp

4/1/2014, 2:52:04 AM

Confirmations

6,339,388

Merkle Root

ddda1c294742cf9ebfcf34cdcba8c671a3e72c68e10749fdbfd534e5e4da03c6
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.

3.560 × 10⁹⁵(96-digit number)
35609353313220237477…67042145184093951039
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
3.560 × 10⁹⁵(96-digit number)
35609353313220237477…67042145184093951039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.121 × 10⁹⁵(96-digit number)
71218706626440474954…34084290368187902079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.424 × 10⁹⁶(97-digit number)
14243741325288094990…68168580736375804159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.848 × 10⁹⁶(97-digit number)
28487482650576189981…36337161472751608319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.697 × 10⁹⁶(97-digit number)
56974965301152379963…72674322945503216639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.139 × 10⁹⁷(98-digit number)
11394993060230475992…45348645891006433279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.278 × 10⁹⁷(98-digit number)
22789986120460951985…90697291782012866559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.557 × 10⁹⁷(98-digit number)
45579972240921903970…81394583564025733119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
9.115 × 10⁹⁷(98-digit number)
91159944481843807941…62789167128051466239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.823 × 10⁹⁸(99-digit number)
18231988896368761588…25578334256102932479
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:57,713,299 XPM·at block #6,808,656 · updates every 60s
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