Block #244,888

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/5/2013, 3:46:13 AM · Difficulty 9.9632 · 6,561,150 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8a8945bca9016856d72e8809bed136690d1d557843c2f1d5f9678f73f50d014e

Height

#244,888

Difficulty

9.963226

Transactions

5

Size

1.11 KB

Version

2

Bits

09f695f4

Nonce

5,294

Timestamp

11/5/2013, 3:46:13 AM

Confirmations

6,561,150

Merkle Root

b777211e4b58d0c49e7b9f71faa605b0ba913dc4c55197afa8986576944aae70
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.

1.112 × 10⁹⁶(97-digit number)
11129557037053470290…29362913631184942079
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
1.112 × 10⁹⁶(97-digit number)
11129557037053470290…29362913631184942079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.225 × 10⁹⁶(97-digit number)
22259114074106940580…58725827262369884159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.451 × 10⁹⁶(97-digit number)
44518228148213881161…17451654524739768319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
8.903 × 10⁹⁶(97-digit number)
89036456296427762322…34903309049479536639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.780 × 10⁹⁷(98-digit number)
17807291259285552464…69806618098959073279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.561 × 10⁹⁷(98-digit number)
35614582518571104928…39613236197918146559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
7.122 × 10⁹⁷(98-digit number)
71229165037142209857…79226472395836293119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.424 × 10⁹⁸(99-digit number)
14245833007428441971…58452944791672586239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.849 × 10⁹⁸(99-digit number)
28491666014856883943…16905889583345172479
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:57,692,384 XPM·at block #6,806,037 · updates every 60s
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