Block #2,152,492

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 6/9/2017, 1:36:06 AM · Difficulty 10.9018 · 4,681,246 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b016847de44e8c7f82718ce8bdb145ec80e4f61ebe9ea55558cda562547d92ca

Height

#2,152,492

Difficulty

10.901796

Transactions

5

Size

1.08 KB

Version

2

Bits

0ae6dc1b

Nonce

1,621,685,858

Timestamp

6/9/2017, 1:36:06 AM

Confirmations

4,681,246

Merkle Root

92fa055323cfd0c40d8a7a54f92a97cb8c1de362e1092d65554dc77f36068e6f
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.

7.667 × 10⁹⁵(96-digit number)
76678865307874741890…11201539488493157759
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
7.667 × 10⁹⁵(96-digit number)
76678865307874741890…11201539488493157759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.533 × 10⁹⁶(97-digit number)
15335773061574948378…22403078976986315519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.067 × 10⁹⁶(97-digit number)
30671546123149896756…44806157953972631039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.134 × 10⁹⁶(97-digit number)
61343092246299793512…89612315907945262079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.226 × 10⁹⁷(98-digit number)
12268618449259958702…79224631815890524159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.453 × 10⁹⁷(98-digit number)
24537236898519917405…58449263631781048319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.907 × 10⁹⁷(98-digit number)
49074473797039834810…16898527263562096639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
9.814 × 10⁹⁷(98-digit number)
98148947594079669620…33797054527124193279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.962 × 10⁹⁸(99-digit number)
19629789518815933924…67594109054248386559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.925 × 10⁹⁸(99-digit number)
39259579037631867848…35188218108496773119
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:57,914,121 XPM·at block #6,833,737 · updates every 60s
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