Block #2,642,896

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 5/1/2018, 9:50:42 PM · Difficulty 11.6674 · 4,189,255 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
80e5dafe6cc0900c752af08109cea46b1102e6f49b610aa3df89cdf980da05ee

Height

#2,642,896

Difficulty

11.667357

Transactions

2

Size

1.46 KB

Version

2

Bits

0baad7ef

Nonce

213,503,013

Timestamp

5/1/2018, 9:50:42 PM

Confirmations

4,189,255

Merkle Root

3a94436b36e9b41a385e76e7cc7bb80c7f9f1023b16f2dbb75d68ff32134d011
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.

5.834 × 10⁹³(94-digit number)
58341158733760187045…67899227007048815359
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
5.834 × 10⁹³(94-digit number)
58341158733760187045…67899227007048815359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.166 × 10⁹⁴(95-digit number)
11668231746752037409…35798454014097630719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.333 × 10⁹⁴(95-digit number)
23336463493504074818…71596908028195261439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.667 × 10⁹⁴(95-digit number)
46672926987008149636…43193816056390522879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
9.334 × 10⁹⁴(95-digit number)
93345853974016299273…86387632112781045759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.866 × 10⁹⁵(96-digit number)
18669170794803259854…72775264225562091519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.733 × 10⁹⁵(96-digit number)
37338341589606519709…45550528451124183039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.467 × 10⁹⁵(96-digit number)
74676683179213039418…91101056902248366079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.493 × 10⁹⁶(97-digit number)
14935336635842607883…82202113804496732159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.987 × 10⁹⁶(97-digit number)
29870673271685215767…64404227608993464319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
5.974 × 10⁹⁶(97-digit number)
59741346543370431534…28808455217986928639
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 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
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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,901,346 XPM·at block #6,832,150 · 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