Block #229,912

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/27/2013, 11:47:59 AM · Difficulty 9.9388 · 6,579,942 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7398f21e666a511a09557c89ea571be339ba76069c4bc912a56b85a926cde720

Height

#229,912

Difficulty

9.938800

Transactions

2

Size

424 B

Version

2

Bits

09f05538

Nonce

49,539

Timestamp

10/27/2013, 11:47:59 AM

Confirmations

6,579,942

Merkle Root

840b5dc3423a5979fa5435f27d2f23a2b56767879d15a51855a3fe684f89d8df
Transactions (2)
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.

6.950 × 10⁹⁴(95-digit number)
69507254993403766443…92911187287737159819
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
6.950 × 10⁹⁴(95-digit number)
69507254993403766443…92911187287737159819
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.390 × 10⁹⁵(96-digit number)
13901450998680753288…85822374575474319639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.780 × 10⁹⁵(96-digit number)
27802901997361506577…71644749150948639279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.560 × 10⁹⁵(96-digit number)
55605803994723013154…43289498301897278559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.112 × 10⁹⁶(97-digit number)
11121160798944602630…86578996603794557119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.224 × 10⁹⁶(97-digit number)
22242321597889205261…73157993207589114239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.448 × 10⁹⁶(97-digit number)
44484643195778410523…46315986415178228479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
8.896 × 10⁹⁶(97-digit number)
88969286391556821047…92631972830356456959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.779 × 10⁹⁷(98-digit number)
17793857278311364209…85263945660712913919
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:57,722,919 XPM·at block #6,809,853 · updates every 60s
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