Block #2,924,907

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 11/16/2018, 4:00:15 AM · Difficulty 11.3557 · 3,918,993 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9c674107ae61e760cb9c30432df1e4768cd550f869b75dfb18eca7672e7a5ce5

Height

#2,924,907

Difficulty

11.355725

Transactions

10

Size

65.63 KB

Version

2

Bits

0b5b10c6

Nonce

1,339,029,164

Timestamp

11/16/2018, 4:00:15 AM

Confirmations

3,918,993

Merkle Root

6b8b9970ae31cf7e824a55df5a901a596cc4e20fc12620d2ba18282f20062165
Transactions (10)
1 in → 1 out8.4600 XPM110 B
50 in → 1 out223.6771 XPM7.27 KB
50 in → 1 out236.4077 XPM7.27 KB
50 in → 1 out222.9348 XPM7.27 KB
50 in → 1 out244.2168 XPM7.27 KB
50 in → 1 out207.2041 XPM7.26 KB
50 in → 1 out216.0790 XPM7.27 KB
50 in → 1 out234.3601 XPM7.27 KB
50 in → 1 out229.8903 XPM7.27 KB
50 in → 1 out232.5149 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.

3.375 × 10⁹⁶(97-digit number)
33752343831657639798…21568313302667745281
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
3.375 × 10⁹⁶(97-digit number)
33752343831657639798…21568313302667745281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.750 × 10⁹⁶(97-digit number)
67504687663315279596…43136626605335490561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.350 × 10⁹⁷(98-digit number)
13500937532663055919…86273253210670981121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.700 × 10⁹⁷(98-digit number)
27001875065326111838…72546506421341962241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.400 × 10⁹⁷(98-digit number)
54003750130652223677…45093012842683924481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.080 × 10⁹⁸(99-digit number)
10800750026130444735…90186025685367848961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.160 × 10⁹⁸(99-digit number)
21601500052260889470…80372051370735697921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.320 × 10⁹⁸(99-digit number)
43203000104521778941…60744102741471395841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
8.640 × 10⁹⁸(99-digit number)
86406000209043557883…21488205482942791681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.728 × 10⁹⁹(100-digit number)
17281200041808711576…42976410965885583361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
3.456 × 10⁹⁹(100-digit number)
34562400083617423153…85952821931771166721
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:57,995,571 XPM·at block #6,843,899 · updates every 60s
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