Block #2,928,964

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 11/18/2018, 8:11:38 PM · Difficulty 11.3818 · 3,914,298 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
117f89ae8cae3c093056f2624a071ca04ed6ddf7a422710e7be38c9ead397a79

Height

#2,928,964

Difficulty

11.381839

Transactions

39

Size

9.61 KB

Version

2

Bits

0b61c02c

Nonce

970,853,648

Timestamp

11/18/2018, 8:11:38 PM

Confirmations

3,914,298

Merkle Root

1489c9dfe5fcdf77fdf0f74a0d7bbf00106119e069f57cbe72430e25af2f0f30
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.

1.515 × 10⁹⁶(97-digit number)
15158434706689747225…82156900324885155841
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
1.515 × 10⁹⁶(97-digit number)
15158434706689747225…82156900324885155841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.031 × 10⁹⁶(97-digit number)
30316869413379494451…64313800649770311681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
6.063 × 10⁹⁶(97-digit number)
60633738826758988903…28627601299540623361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.212 × 10⁹⁷(98-digit number)
12126747765351797780…57255202599081246721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.425 × 10⁹⁷(98-digit number)
24253495530703595561…14510405198162493441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.850 × 10⁹⁷(98-digit number)
48506991061407191122…29020810396324986881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
9.701 × 10⁹⁷(98-digit number)
97013982122814382244…58041620792649973761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.940 × 10⁹⁸(99-digit number)
19402796424562876448…16083241585299947521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.880 × 10⁹⁸(99-digit number)
38805592849125752897…32166483170599895041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.761 × 10⁹⁸(99-digit number)
77611185698251505795…64332966341199790081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.552 × 10⁹⁹(100-digit number)
15522237139650301159…28665932682399580161
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:57,990,469 XPM·at block #6,843,261 · updates every 60s
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