Block #2,076,289

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/18/2017, 3:40:06 PM · Difficulty 10.8456 · 4,766,965 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ccdd632798e46559d2bdc9c24142002973aa50a02684d3783283ff146789837c

Height

#2,076,289

Difficulty

10.845638

Transactions

2

Size

1.14 KB

Version

2

Bits

0ad87bb7

Nonce

552,712,757

Timestamp

4/18/2017, 3:40:06 PM

Confirmations

4,766,965

Merkle Root

d979348b09d6b0e89ee54fa9e12f2d4abfe4283f62b63c1fbfdca513d5bd5245
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.

1.065 × 10⁹⁶(97-digit number)
10653378916148904167…66885692693772974079
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
1.065 × 10⁹⁶(97-digit number)
10653378916148904167…66885692693772974079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.130 × 10⁹⁶(97-digit number)
21306757832297808335…33771385387545948159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.261 × 10⁹⁶(97-digit number)
42613515664595616670…67542770775091896319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
8.522 × 10⁹⁶(97-digit number)
85227031329191233341…35085541550183792639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.704 × 10⁹⁷(98-digit number)
17045406265838246668…70171083100367585279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.409 × 10⁹⁷(98-digit number)
34090812531676493336…40342166200735170559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.818 × 10⁹⁷(98-digit number)
68181625063352986672…80684332401470341119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.363 × 10⁹⁸(99-digit number)
13636325012670597334…61368664802940682239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.727 × 10⁹⁸(99-digit number)
27272650025341194669…22737329605881364479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
5.454 × 10⁹⁸(99-digit number)
54545300050682389338…45474659211762728959
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:57,990,409 XPM·at block #6,843,253 · 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