Block #276,924

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/27/2013, 9:29:52 AM · Difficulty 9.9646 · 6,528,872 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d6cd609fd9e90819c37a6a4e38f8dc2ae9198095fe626a5ade42a84bfb1bfe5f

Height

#276,924

Difficulty

9.964646

Transactions

1

Size

1001 B

Version

2

Bits

09f6f30e

Nonce

89,529

Timestamp

11/27/2013, 9:29:52 AM

Confirmations

6,528,872

Merkle Root

d6ce0b01f0deafa2498ef49c41d9c03d38e8a3a11b7b56cb21a467e55b995c72
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.

1.279 × 10⁹⁰(91-digit number)
12799783131955458237…45077492467689000159
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
1.279 × 10⁹⁰(91-digit number)
12799783131955458237…45077492467689000159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.559 × 10⁹⁰(91-digit number)
25599566263910916475…90154984935378000319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.119 × 10⁹⁰(91-digit number)
51199132527821832951…80309969870756000639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.023 × 10⁹¹(92-digit number)
10239826505564366590…60619939741512001279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.047 × 10⁹¹(92-digit number)
20479653011128733180…21239879483024002559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.095 × 10⁹¹(92-digit number)
40959306022257466361…42479758966048005119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
8.191 × 10⁹¹(92-digit number)
81918612044514932722…84959517932096010239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.638 × 10⁹²(93-digit number)
16383722408902986544…69919035864192020479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.276 × 10⁹²(93-digit number)
32767444817805973089…39838071728384040959
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:57,690,452 XPM·at block #6,805,795 · updates every 60s
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