Block #2,392,663

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/24/2017, 4:29:02 AM · Difficulty 10.8715 · 4,448,703 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
eb24c716a6afcc4928793415a2f4a63904b2d1a470215a2672799b04e52ea21d

Height

#2,392,663

Difficulty

10.871462

Transactions

3

Size

719 B

Version

2

Bits

0adf181d

Nonce

1,033,834,330

Timestamp

11/24/2017, 4:29:02 AM

Confirmations

4,448,703

Merkle Root

e2677c91c5fe0be27b9e8c2ce116a76f9d1072ad915b4db27dc073feac2392bc
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.

2.881 × 10⁹⁵(96-digit number)
28816125912678889272…56037946334840907839
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
2.881 × 10⁹⁵(96-digit number)
28816125912678889272…56037946334840907839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
5.763 × 10⁹⁵(96-digit number)
57632251825357778544…12075892669681815679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.152 × 10⁹⁶(97-digit number)
11526450365071555708…24151785339363631359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.305 × 10⁹⁶(97-digit number)
23052900730143111417…48303570678727262719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.610 × 10⁹⁶(97-digit number)
46105801460286222835…96607141357454525439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
9.221 × 10⁹⁶(97-digit number)
92211602920572445670…93214282714909050879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.844 × 10⁹⁷(98-digit number)
18442320584114489134…86428565429818101759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.688 × 10⁹⁷(98-digit number)
36884641168228978268…72857130859636203519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
7.376 × 10⁹⁷(98-digit number)
73769282336457956536…45714261719272407039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.475 × 10⁹⁸(99-digit number)
14753856467291591307…91428523438544814079
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:57,975,297 XPM·at block #6,841,365 · updates every 60s
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