Block #236,999

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/31/2013, 7:20:32 PM · Difficulty 9.9489 · 6,565,493 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d374433417311d1e4e42ceb1f5da405706c185edbdfaea8c345fac0554767ad1

Height

#236,999

Difficulty

9.948871

Transactions

4

Size

1.00 KB

Version

2

Bits

09f2e934

Nonce

81,632

Timestamp

10/31/2013, 7:20:32 PM

Confirmations

6,565,493

Merkle Root

4609228f1f6568c7621372aa5002dd85c66106f95e595e44a5bbeb8ead67502c
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.

1.262 × 10⁹⁶(97-digit number)
12629393380865579603…56217025131400104959
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
1.262 × 10⁹⁶(97-digit number)
12629393380865579603…56217025131400104959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.525 × 10⁹⁶(97-digit number)
25258786761731159207…12434050262800209919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.051 × 10⁹⁶(97-digit number)
50517573523462318415…24868100525600419839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.010 × 10⁹⁷(98-digit number)
10103514704692463683…49736201051200839679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.020 × 10⁹⁷(98-digit number)
20207029409384927366…99472402102401679359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.041 × 10⁹⁷(98-digit number)
40414058818769854732…98944804204803358719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
8.082 × 10⁹⁷(98-digit number)
80828117637539709464…97889608409606717439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.616 × 10⁹⁸(99-digit number)
16165623527507941892…95779216819213434879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.233 × 10⁹⁸(99-digit number)
32331247055015883785…91558433638426869759
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:57,663,950 XPM·at block #6,802,491 · updates every 60s
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