Block #2,460,832

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/6/2018, 10:49:55 PM · Difficulty 10.9550 · 4,365,743 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6aded9d7ba28350a6a1913c17a486f4fbd47c1cfce92ec5ef9449ed843871553

Height

#2,460,832

Difficulty

10.954954

Transactions

1

Size

238 B

Version

2

Bits

0af477e1

Nonce

268,316

Timestamp

1/6/2018, 10:49:55 PM

Confirmations

4,365,743

Merkle Root

e6d2b5cfd79f9df8a2b426d4ba544d0d5e8cd2ea106e38c9411e21c891f02098
Transactions (1)
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.

5.071 × 10¹⁰¹(102-digit number)
50717104156167810536…88672911948206602241
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
5.071 × 10¹⁰¹(102-digit number)
50717104156167810536…88672911948206602241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.014 × 10¹⁰²(103-digit number)
10143420831233562107…77345823896413204481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.028 × 10¹⁰²(103-digit number)
20286841662467124214…54691647792826408961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.057 × 10¹⁰²(103-digit number)
40573683324934248429…09383295585652817921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.114 × 10¹⁰²(103-digit number)
81147366649868496858…18766591171305635841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.622 × 10¹⁰³(104-digit number)
16229473329973699371…37533182342611271681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.245 × 10¹⁰³(104-digit number)
32458946659947398743…75066364685222543361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.491 × 10¹⁰³(104-digit number)
64917893319894797487…50132729370445086721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.298 × 10¹⁰⁴(105-digit number)
12983578663978959497…00265458740890173441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.596 × 10¹⁰⁴(105-digit number)
25967157327957918994…00530917481780346881
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:57,856,749 XPM·at block #6,826,574 · updates every 60s
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