Block #1,626,207

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 6/13/2016, 6:46:48 AM · Difficulty 10.5868 · 5,200,446 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3ce02f2ae243386629b5aedeff7faf43496469eecafc1e4caf7d9d9a2f26784f

Height

#1,626,207

Difficulty

10.586802

Transactions

2

Size

5.33 KB

Version

2

Bits

0a9638a3

Nonce

252,410,147

Timestamp

6/13/2016, 6:46:48 AM

Confirmations

5,200,446

Merkle Root

e499d6f02189c935464ab6268ab1c6d93cea2ee813a4eb349fb0c07ae70eca8b
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.

1.632 × 10⁹³(94-digit number)
16322018120713099982…92788181464951854119
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
1.632 × 10⁹³(94-digit number)
16322018120713099982…92788181464951854119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.264 × 10⁹³(94-digit number)
32644036241426199964…85576362929903708239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.528 × 10⁹³(94-digit number)
65288072482852399928…71152725859807416479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.305 × 10⁹⁴(95-digit number)
13057614496570479985…42305451719614832959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.611 × 10⁹⁴(95-digit number)
26115228993140959971…84610903439229665919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.223 × 10⁹⁴(95-digit number)
52230457986281919943…69221806878459331839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.044 × 10⁹⁵(96-digit number)
10446091597256383988…38443613756918663679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.089 × 10⁹⁵(96-digit number)
20892183194512767977…76887227513837327359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.178 × 10⁹⁵(96-digit number)
41784366389025535954…53774455027674654719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
8.356 × 10⁹⁵(96-digit number)
83568732778051071908…07548910055349309439
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:57,857,373 XPM·at block #6,826,652 · updates every 60s
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