Block #208,326

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 10/13/2013, 10:56:20 PM · Difficulty 9.9058 · 6,604,510 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e0fafa364dc1ac6adbb37a179ae1f6e0fd656d8d254bb1a6096e9c3a01e26999

Height

#208,326

Difficulty

9.905839

Transactions

3

Size

962 B

Version

2

Bits

09e7e50e

Nonce

99,652

Timestamp

10/13/2013, 10:56:20 PM

Confirmations

6,604,510

Merkle Root

b6186408cdca6f898602a1021c39b3755e64e2ca72e044cd38da84f9b50bde4f
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.

4.090 × 10⁹⁴(95-digit number)
40904572888967196337…31113541716370104319
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
4.090 × 10⁹⁴(95-digit number)
40904572888967196337…31113541716370104319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
8.180 × 10⁹⁴(95-digit number)
81809145777934392674…62227083432740208639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.636 × 10⁹⁵(96-digit number)
16361829155586878534…24454166865480417279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.272 × 10⁹⁵(96-digit number)
32723658311173757069…48908333730960834559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
6.544 × 10⁹⁵(96-digit number)
65447316622347514139…97816667461921669119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.308 × 10⁹⁶(97-digit number)
13089463324469502827…95633334923843338239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.617 × 10⁹⁶(97-digit number)
26178926648939005655…91266669847686676479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.235 × 10⁹⁶(97-digit number)
52357853297878011311…82533339695373352959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.047 × 10⁹⁷(98-digit number)
10471570659575602262…65066679390746705919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.094 × 10⁹⁷(98-digit number)
20943141319151204524…30133358781493411839
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:57,746,733 XPM·at block #6,812,835 · updates every 60s
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