Block #236,604

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/31/2013, 2:10:55 PM · Difficulty 9.9480 · 6,573,134 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2abb950804b3c29822d68c8642c66b55a9d727225eb6f39161d98f62f3266735

Height

#236,604

Difficulty

9.947989

Transactions

5

Size

2.84 KB

Version

2

Bits

09f2af69

Nonce

18,103

Timestamp

10/31/2013, 2:10:55 PM

Confirmations

6,573,134

Merkle Root

f68584e5c85e79d9cdb7edff9c36ddae37289396f6f865180ab6e8ab6b5d8cdd
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.

6.051 × 10⁹⁶(97-digit number)
60519099334826402743…45973182624175718399
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
6.051 × 10⁹⁶(97-digit number)
60519099334826402743…45973182624175718399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.210 × 10⁹⁷(98-digit number)
12103819866965280548…91946365248351436799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.420 × 10⁹⁷(98-digit number)
24207639733930561097…83892730496702873599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.841 × 10⁹⁷(98-digit number)
48415279467861122194…67785460993405747199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
9.683 × 10⁹⁷(98-digit number)
96830558935722244389…35570921986811494399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.936 × 10⁹⁸(99-digit number)
19366111787144448877…71141843973622988799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.873 × 10⁹⁸(99-digit number)
38732223574288897755…42283687947245977599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.746 × 10⁹⁸(99-digit number)
77464447148577795511…84567375894491955199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.549 × 10⁹⁹(100-digit number)
15492889429715559102…69134751788983910399
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:57,721,987 XPM·at block #6,809,737 · updates every 60s
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