Block #244,306

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/4/2013, 7:00:16 PM · Difficulty 9.9628 · 6,597,904 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e276299605d4e199b816a65f52156a88f1d06bd44aefd2df50cee8b9f2100f9e

Height

#244,306

Difficulty

9.962791

Transactions

2

Size

2.51 KB

Version

2

Bits

09f6797a

Nonce

2,111

Timestamp

11/4/2013, 7:00:16 PM

Confirmations

6,597,904

Merkle Root

f9b002ed9156356171feb9eede6c6c19132cc161b3e3a8f22fd2263563ba139a
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.

3.015 × 10⁹⁴(95-digit number)
30158379770390357883…11907395378716912639
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
3.015 × 10⁹⁴(95-digit number)
30158379770390357883…11907395378716912639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
6.031 × 10⁹⁴(95-digit number)
60316759540780715767…23814790757433825279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.206 × 10⁹⁵(96-digit number)
12063351908156143153…47629581514867650559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.412 × 10⁹⁵(96-digit number)
24126703816312286307…95259163029735301119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.825 × 10⁹⁵(96-digit number)
48253407632624572614…90518326059470602239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
9.650 × 10⁹⁵(96-digit number)
96506815265249145228…81036652118941204479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.930 × 10⁹⁶(97-digit number)
19301363053049829045…62073304237882408959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.860 × 10⁹⁶(97-digit number)
38602726106099658091…24146608475764817919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
7.720 × 10⁹⁶(97-digit number)
77205452212199316182…48293216951529635839
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:57,982,076 XPM·at block #6,842,209 · updates every 60s
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