Block #2,160,504

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 6/14/2017, 3:38:42 PM · Difficulty 10.9015 · 4,666,487 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
12fe7ffa476a89c577a2b4dbf48c1ffb4d896a09406df2edfbec1243a9250419

Height

#2,160,504

Difficulty

10.901472

Transactions

3

Size

10.50 KB

Version

2

Bits

0ae6c6de

Nonce

296,034,477

Timestamp

6/14/2017, 3:38:42 PM

Confirmations

4,666,487

Merkle Root

5752f3901bfc82d878a8b69927ca5c9e51260cf447e0eccf4783dbf5365d0105
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.

3.062 × 10⁹⁵(96-digit number)
30629699482896556799…07604034532684482559
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
3.062 × 10⁹⁵(96-digit number)
30629699482896556799…07604034532684482559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
6.125 × 10⁹⁵(96-digit number)
61259398965793113599…15208069065368965119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.225 × 10⁹⁶(97-digit number)
12251879793158622719…30416138130737930239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.450 × 10⁹⁶(97-digit number)
24503759586317245439…60832276261475860479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.900 × 10⁹⁶(97-digit number)
49007519172634490879…21664552522951720959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
9.801 × 10⁹⁶(97-digit number)
98015038345268981759…43329105045903441919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.960 × 10⁹⁷(98-digit number)
19603007669053796351…86658210091806883839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.920 × 10⁹⁷(98-digit number)
39206015338107592703…73316420183613767679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
7.841 × 10⁹⁷(98-digit number)
78412030676215185407…46632840367227535359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.568 × 10⁹⁸(99-digit number)
15682406135243037081…93265680734455070719
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:57,860,103 XPM·at block #6,826,990 · updates every 60s
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