Block #2,924,825

2CCLength 12★★★★☆

Cunningham Chain of the Second Kind · Discovered 11/16/2018, 2:27:14 AM · Difficulty 11.3573 · 3,914,848 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
245671d500e87d2e0519540f19ca23d2daf1164cf64e94d41d252ffc01e4924d

Height

#2,924,825

Difficulty

11.357325

Transactions

13

Size

73.52 KB

Version

2

Bits

0b5b79ad

Nonce

876,433,537

Timestamp

11/16/2018, 2:27:14 AM

Confirmations

3,914,848

Merkle Root

1bed1704f9ad42050bcb7bec02a3a1a5ff000b80d032d6fd240f65751ab22521
Transactions (13)
1 in → 1 out8.5600 XPM110 B
50 in → 1 out233.5257 XPM7.27 KB
50 in → 1 out238.8165 XPM7.27 KB
50 in → 1 out215.5280 XPM7.27 KB
50 in → 1 out241.4027 XPM7.27 KB
50 in → 1 out229.3736 XPM7.27 KB
50 in → 1 out233.6589 XPM7.27 KB
50 in → 1 out224.9050 XPM7.27 KB
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.

5.917 × 10⁹⁵(96-digit number)
59173417615097871666…16825989789539388161
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
5.917 × 10⁹⁵(96-digit number)
59173417615097871666…16825989789539388161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.183 × 10⁹⁶(97-digit number)
11834683523019574333…33651979579078776321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.366 × 10⁹⁶(97-digit number)
23669367046039148666…67303959158157552641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.733 × 10⁹⁶(97-digit number)
47338734092078297332…34607918316315105281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
9.467 × 10⁹⁶(97-digit number)
94677468184156594665…69215836632630210561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.893 × 10⁹⁷(98-digit number)
18935493636831318933…38431673265260421121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.787 × 10⁹⁷(98-digit number)
37870987273662637866…76863346530520842241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.574 × 10⁹⁷(98-digit number)
75741974547325275732…53726693061041684481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.514 × 10⁹⁸(99-digit number)
15148394909465055146…07453386122083368961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.029 × 10⁹⁸(99-digit number)
30296789818930110293…14906772244166737921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
6.059 × 10⁹⁸(99-digit number)
60593579637860220586…29813544488333475841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
12
2^11 × origin + 1
1.211 × 10⁹⁹(100-digit number)
12118715927572044117…59627088976666951681
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,961,673 XPM·at block #6,839,672 · updates every 60s
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