Block #280,379

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/28/2013, 4:10:55 PM · Difficulty 9.9744 · 6,528,101 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cbe17ce758c8ccaf6821aa6971465377f1525a48f3f19733d1e391fa6b93085b

Height

#280,379

Difficulty

9.974366

Transactions

1

Size

1.15 KB

Version

2

Bits

09f9700d

Nonce

25,171

Timestamp

11/28/2013, 4:10:55 PM

Confirmations

6,528,101

Merkle Root

1273359fd25d588650f6ac34954d1d982e7728448ade8e4e9db25287e4334770
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.

2.605 × 10⁹⁴(95-digit number)
26053805516433568330…47342650869995238401
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
2.605 × 10⁹⁴(95-digit number)
26053805516433568330…47342650869995238401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.210 × 10⁹⁴(95-digit number)
52107611032867136660…94685301739990476801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.042 × 10⁹⁵(96-digit number)
10421522206573427332…89370603479980953601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.084 × 10⁹⁵(96-digit number)
20843044413146854664…78741206959961907201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.168 × 10⁹⁵(96-digit number)
41686088826293709328…57482413919923814401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
8.337 × 10⁹⁵(96-digit number)
83372177652587418656…14964827839847628801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.667 × 10⁹⁶(97-digit number)
16674435530517483731…29929655679695257601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.334 × 10⁹⁶(97-digit number)
33348871061034967462…59859311359390515201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.669 × 10⁹⁶(97-digit number)
66697742122069934925…19718622718781030401
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,711,890 XPM·at block #6,808,479 · updates every 60s
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