Block #377,943

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 1/27/2014, 11:48:44 AM · Difficulty 10.4203 · 6,439,997 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
743a395af255b19df108b6814a3dcb7a3bb1c6c5863255a21f471e6c12ccddc9

Height

#377,943

Difficulty

10.420326

Transactions

2

Size

1.47 KB

Version

2

Bits

0a6b9a74

Nonce

35,259

Timestamp

1/27/2014, 11:48:44 AM

Confirmations

6,439,997

Merkle Root

dd6f5676bb952eb416a53f7cd23bbf56458c5d160c31e5f3b4578c653f2a2dac
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.

1.375 × 10⁹⁹(100-digit number)
13758911109350052513…96548655327458816001
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
1.375 × 10⁹⁹(100-digit number)
13758911109350052513…96548655327458816001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.751 × 10⁹⁹(100-digit number)
27517822218700105026…93097310654917632001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.503 × 10⁹⁹(100-digit number)
55035644437400210053…86194621309835264001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.100 × 10¹⁰⁰(101-digit number)
11007128887480042010…72389242619670528001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.201 × 10¹⁰⁰(101-digit number)
22014257774960084021…44778485239341056001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.402 × 10¹⁰⁰(101-digit number)
44028515549920168042…89556970478682112001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.805 × 10¹⁰⁰(101-digit number)
88057031099840336084…79113940957364224001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.761 × 10¹⁰¹(102-digit number)
17611406219968067216…58227881914728448001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.522 × 10¹⁰¹(102-digit number)
35222812439936134433…16455763829456896001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.044 × 10¹⁰¹(102-digit number)
70445624879872268867…32911527658913792001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.408 × 10¹⁰²(103-digit number)
14089124975974453773…65823055317827584001
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:57,787,586 XPM·at block #6,817,939 · 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