Block #2,479,099

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 1/18/2018, 5:12:45 PM · Difficulty 10.9659 · 4,363,759 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8ccaa60baf983e250831ab2f5de9b20c367d7dc899e162afd75aaca8d12491fd

Height

#2,479,099

Difficulty

10.965851

Transactions

2

Size

640 B

Version

2

Bits

0af74206

Nonce

471,175,006

Timestamp

1/18/2018, 5:12:45 PM

Confirmations

4,363,759

Merkle Root

26a9d43bb44cdc87a059afc1fab8462223d052dc06548a341ac9dfd10f547baa
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.

1.669 × 10⁹⁵(96-digit number)
16696817006049755823…18405694938388460481
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
1.669 × 10⁹⁵(96-digit number)
16696817006049755823…18405694938388460481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.339 × 10⁹⁵(96-digit number)
33393634012099511646…36811389876776920961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
6.678 × 10⁹⁵(96-digit number)
66787268024199023292…73622779753553841921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.335 × 10⁹⁶(97-digit number)
13357453604839804658…47245559507107683841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.671 × 10⁹⁶(97-digit number)
26714907209679609317…94491119014215367681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.342 × 10⁹⁶(97-digit number)
53429814419359218634…88982238028430735361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.068 × 10⁹⁷(98-digit number)
10685962883871843726…77964476056861470721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.137 × 10⁹⁷(98-digit number)
21371925767743687453…55928952113722941441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.274 × 10⁹⁷(98-digit number)
42743851535487374907…11857904227445882881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
8.548 × 10⁹⁷(98-digit number)
85487703070974749814…23715808454891765761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.709 × 10⁹⁸(99-digit number)
17097540614194949962…47431616909783531521
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:57,987,211 XPM·at block #6,842,857 · updates every 60s
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