Block #2,465,038

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 1/9/2018, 11:40:25 AM · Difficulty 10.9598 · 4,377,261 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bfaa189b01985fbc0942f88e820a510646d0ce80ed3f482af32cd18a47aa09c8

Height

#2,465,038

Difficulty

10.959772

Transactions

2

Size

571 B

Version

2

Bits

0af5b3a3

Nonce

53,161,264

Timestamp

1/9/2018, 11:40:25 AM

Confirmations

4,377,261

Merkle Root

78580c7be2a7f8c2945ea75aa90207635fe4cde483829776d2e19c45301d2630
Transactions (2)
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.

1.622 × 10⁹³(94-digit number)
16224621238869374171…16846095038309912639
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
1.622 × 10⁹³(94-digit number)
16224621238869374171…16846095038309912639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.244 × 10⁹³(94-digit number)
32449242477738748342…33692190076619825279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.489 × 10⁹³(94-digit number)
64898484955477496685…67384380153239650559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.297 × 10⁹⁴(95-digit number)
12979696991095499337…34768760306479301119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.595 × 10⁹⁴(95-digit number)
25959393982190998674…69537520612958602239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.191 × 10⁹⁴(95-digit number)
51918787964381997348…39075041225917204479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.038 × 10⁹⁵(96-digit number)
10383757592876399469…78150082451834408959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.076 × 10⁹⁵(96-digit number)
20767515185752798939…56300164903668817919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.153 × 10⁹⁵(96-digit number)
41535030371505597878…12600329807337635839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
8.307 × 10⁹⁵(96-digit number)
83070060743011195756…25200659614675271679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.661 × 10⁹⁶(97-digit number)
16614012148602239151…50401319229350543359
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,982,796 XPM·at block #6,842,298 · updates every 60s
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