Block #229,009

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/26/2013, 9:57:08 PM · Difficulty 9.9379 · 6,580,918 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7fd213508ac0d1d9ed4b2e47e224545b6d07ff1f7facf5879c310b18920fab05

Height

#229,009

Difficulty

9.937894

Transactions

2

Size

3.51 KB

Version

2

Bits

09f019d0

Nonce

898

Timestamp

10/26/2013, 9:57:08 PM

Confirmations

6,580,918

Merkle Root

502410e0fe2399ed16a01acb308c206cb3917d05d9de3423824d9de3f21e97f5
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.

6.763 × 10⁹⁴(95-digit number)
67632387229654819273…02051139289360618139
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
6.763 × 10⁹⁴(95-digit number)
67632387229654819273…02051139289360618139
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.352 × 10⁹⁵(96-digit number)
13526477445930963854…04102278578721236279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.705 × 10⁹⁵(96-digit number)
27052954891861927709…08204557157442472559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.410 × 10⁹⁵(96-digit number)
54105909783723855418…16409114314884945119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.082 × 10⁹⁶(97-digit number)
10821181956744771083…32818228629769890239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.164 × 10⁹⁶(97-digit number)
21642363913489542167…65636457259539780479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.328 × 10⁹⁶(97-digit number)
43284727826979084334…31272914519079560959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
8.656 × 10⁹⁶(97-digit number)
86569455653958168669…62545829038159121919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.731 × 10⁹⁷(98-digit number)
17313891130791633733…25091658076318243839
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,723,502 XPM·at block #6,809,926 · updates every 60s
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