Block #469,000

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/31/2014, 9:47:34 PM · Difficulty 10.4316 · 6,325,874 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
eceaefe604581f15cc725f96001d0fe3650ac8cdd3ebbf45e772b0bda0c5d9c3

Height

#469,000

Difficulty

10.431587

Transactions

3

Size

806 B

Version

2

Bits

0a6e7c74

Nonce

100,666,712

Timestamp

3/31/2014, 9:47:34 PM

Confirmations

6,325,874

Merkle Root

9e10db50e25b59a9bd76b78f51e5acc94fa1f0ba687a2dc178eb9498ad9d078b
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.

7.423 × 10⁹⁴(95-digit number)
74233833037054016262…69763414758849499981
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
7.423 × 10⁹⁴(95-digit number)
74233833037054016262…69763414758849499981
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.484 × 10⁹⁵(96-digit number)
14846766607410803252…39526829517698999961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.969 × 10⁹⁵(96-digit number)
29693533214821606504…79053659035397999921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.938 × 10⁹⁵(96-digit number)
59387066429643213009…58107318070795999841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.187 × 10⁹⁶(97-digit number)
11877413285928642601…16214636141591999681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.375 × 10⁹⁶(97-digit number)
23754826571857285203…32429272283183999361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.750 × 10⁹⁶(97-digit number)
47509653143714570407…64858544566367998721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.501 × 10⁹⁶(97-digit number)
95019306287429140815…29717089132735997441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.900 × 10⁹⁷(98-digit number)
19003861257485828163…59434178265471994881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.800 × 10⁹⁷(98-digit number)
38007722514971656326…18868356530943989761
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 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
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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,603,025 XPM·at block #6,794,873 · updates every 60s
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