Block #1,231,484

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 9/11/2015, 8:17:41 AM · Difficulty 10.7384 · 5,594,175 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
98a8e976e6c0888b06bbfb7938bbf460d1ef82c3defc0a42c25eece7441c4c59

Height

#1,231,484

Difficulty

10.738352

Transactions

2

Size

434 B

Version

2

Bits

0abd04a6

Nonce

439,572,112

Timestamp

9/11/2015, 8:17:41 AM

Confirmations

5,594,175

Merkle Root

a80c9df94f93bb48094c2bdf93dcf6fcd640f4b27084c2d70a6a9039528b54a1
Transactions (2)
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.

9.114 × 10⁹⁶(97-digit number)
91140661313983433455…32063961349032140799
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
9.114 × 10⁹⁶(97-digit number)
91140661313983433455…32063961349032140799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.822 × 10⁹⁷(98-digit number)
18228132262796686691…64127922698064281599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.645 × 10⁹⁷(98-digit number)
36456264525593373382…28255845396128563199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.291 × 10⁹⁷(98-digit number)
72912529051186746764…56511690792257126399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.458 × 10⁹⁸(99-digit number)
14582505810237349352…13023381584514252799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.916 × 10⁹⁸(99-digit number)
29165011620474698705…26046763169028505599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.833 × 10⁹⁸(99-digit number)
58330023240949397411…52093526338057011199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.166 × 10⁹⁹(100-digit number)
11666004648189879482…04187052676114022399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.333 × 10⁹⁹(100-digit number)
23332009296379758964…08374105352228044799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.666 × 10⁹⁹(100-digit number)
46664018592759517929…16748210704456089599
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,849,379 XPM·at block #6,825,658 · 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