Block #280,208

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/28/2013, 2:51:53 PM · Difficulty 9.9739 · 6,511,431 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8af4bb3e7424fde1b2b4d6dc2cea518181306328b3340f51e280de62462210a9

Height

#280,208

Difficulty

9.973894

Transactions

3

Size

947 B

Version

2

Bits

09f95116

Nonce

181,761

Timestamp

11/28/2013, 2:51:53 PM

Confirmations

6,511,431

Merkle Root

cbcf983f1cd4a7e68b0bda20a17a57d2f3252d95e0de7245b5912cb2d63c31f9
Transactions (3)
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.

4.803 × 10⁹³(94-digit number)
48033244759559122129…59836147370025475899
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
4.803 × 10⁹³(94-digit number)
48033244759559122129…59836147370025475899
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
9.606 × 10⁹³(94-digit number)
96066489519118244258…19672294740050951799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.921 × 10⁹⁴(95-digit number)
19213297903823648851…39344589480101903599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.842 × 10⁹⁴(95-digit number)
38426595807647297703…78689178960203807199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
7.685 × 10⁹⁴(95-digit number)
76853191615294595406…57378357920407614399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.537 × 10⁹⁵(96-digit number)
15370638323058919081…14756715840815228799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.074 × 10⁹⁵(96-digit number)
30741276646117838162…29513431681630457599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
6.148 × 10⁹⁵(96-digit number)
61482553292235676325…59026863363260915199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.229 × 10⁹⁶(97-digit number)
12296510658447135265…18053726726521830399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.459 × 10⁹⁶(97-digit number)
24593021316894270530…36107453453043660799
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,577,061 XPM·at block #6,791,638 · updates every 60s
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