Block #375,638

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/25/2014, 8:33:06 PM · Difficulty 10.4249 · 6,438,532 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d00c39a7380c17fc3a9a60832fc72b5498a0eb08b991e6bafddcfd32463dffd2

Height

#375,638

Difficulty

10.424931

Transactions

5

Size

1.09 KB

Version

2

Bits

0a6cc849

Nonce

75,440

Timestamp

1/25/2014, 8:33:06 PM

Confirmations

6,438,532

Merkle Root

5ff9ccc1028a4167b63a9a2d625dde5936c2bd06bd8e1b2598029ef8dcfd8516
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.

5.756 × 10¹⁰⁶(107-digit number)
57562435286745823326…25354710042754063361
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
5.756 × 10¹⁰⁶(107-digit number)
57562435286745823326…25354710042754063361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.151 × 10¹⁰⁷(108-digit number)
11512487057349164665…50709420085508126721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.302 × 10¹⁰⁷(108-digit number)
23024974114698329330…01418840171016253441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.604 × 10¹⁰⁷(108-digit number)
46049948229396658660…02837680342032506881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
9.209 × 10¹⁰⁷(108-digit number)
92099896458793317321…05675360684065013761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.841 × 10¹⁰⁸(109-digit number)
18419979291758663464…11350721368130027521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.683 × 10¹⁰⁸(109-digit number)
36839958583517326928…22701442736260055041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.367 × 10¹⁰⁸(109-digit number)
73679917167034653857…45402885472520110081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.473 × 10¹⁰⁹(110-digit number)
14735983433406930771…90805770945040220161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.947 × 10¹⁰⁹(110-digit number)
29471966866813861543…81611541890080440321
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:57,757,431 XPM·at block #6,814,169 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy Policy·

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

·Privacy Policy