Block #373,337

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/24/2014, 6:04:12 AM · Difficulty 10.4249 · 6,439,704 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ac4f95026b3601d00ebae0f0dd9bde69c342ac8e009594a249e0286ea81c9d00

Height

#373,337

Difficulty

10.424909

Transactions

2

Size

447 B

Version

2

Bits

0a6cc6d9

Nonce

14,822

Timestamp

1/24/2014, 6:04:12 AM

Confirmations

6,439,704

Merkle Root

934380cfa85462b83391a9510a1951f051e74c17a61d0120ae4c2769c64a0150
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.

5.409 × 10⁹⁶(97-digit number)
54099167843718350921…51658297949672229361
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
5.409 × 10⁹⁶(97-digit number)
54099167843718350921…51658297949672229361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.081 × 10⁹⁷(98-digit number)
10819833568743670184…03316595899344458721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.163 × 10⁹⁷(98-digit number)
21639667137487340368…06633191798688917441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.327 × 10⁹⁷(98-digit number)
43279334274974680737…13266383597377834881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.655 × 10⁹⁷(98-digit number)
86558668549949361474…26532767194755669761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.731 × 10⁹⁸(99-digit number)
17311733709989872294…53065534389511339521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.462 × 10⁹⁸(99-digit number)
34623467419979744589…06131068779022679041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.924 × 10⁹⁸(99-digit number)
69246934839959489179…12262137558045358081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.384 × 10⁹⁹(100-digit number)
13849386967991897835…24524275116090716161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.769 × 10⁹⁹(100-digit number)
27698773935983795671…49048550232181432321
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,748,372 XPM·at block #6,813,040 · updates every 60s
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