Block #2,460,263

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 1/6/2018, 2:13:11 PM · Difficulty 10.9545 · 4,381,990 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c88735cd561b0ed34bb8d1d9d5461edd1a7cdeff837f920d78f05a5eeb3302c2

Height

#2,460,263

Difficulty

10.954525

Transactions

57

Size

16.86 KB

Version

2

Bits

0af45bba

Nonce

1,103,953,757

Timestamp

1/6/2018, 2:13:11 PM

Confirmations

4,381,990

Merkle Root

6aa952e1d02487cc82057da7bde67acc733907a5132c4f9ed7681679c523005a
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.

5.057 × 10⁹⁵(96-digit number)
50571572137796501613…88698897985666908161
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
5.057 × 10⁹⁵(96-digit number)
50571572137796501613…88698897985666908161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.011 × 10⁹⁶(97-digit number)
10114314427559300322…77397795971333816321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.022 × 10⁹⁶(97-digit number)
20228628855118600645…54795591942667632641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.045 × 10⁹⁶(97-digit number)
40457257710237201290…09591183885335265281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.091 × 10⁹⁶(97-digit number)
80914515420474402580…19182367770670530561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.618 × 10⁹⁷(98-digit number)
16182903084094880516…38364735541341061121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.236 × 10⁹⁷(98-digit number)
32365806168189761032…76729471082682122241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.473 × 10⁹⁷(98-digit number)
64731612336379522064…53458942165364244481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.294 × 10⁹⁸(99-digit number)
12946322467275904412…06917884330728488961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.589 × 10⁹⁸(99-digit number)
25892644934551808825…13835768661456977921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
5.178 × 10⁹⁸(99-digit number)
51785289869103617651…27671537322913955841
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 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
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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,982,421 XPM·at block #6,842,252 · updates every 60s
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