Block #1,603,870

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 5/28/2016, 3:56:07 PM · Difficulty 10.5983 · 5,221,153 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c9f6eb5b1626e7f3d482934c1e50d066985f2d89858682f3fd39103a3563f91e

Height

#1,603,870

Difficulty

10.598263

Transactions

2

Size

1.38 KB

Version

2

Bits

0a9927bc

Nonce

2,061,289,879

Timestamp

5/28/2016, 3:56:07 PM

Confirmations

5,221,153

Merkle Root

4840d7cbd27fe5c2612f191fce78eceb88987afb33551deee2d8ef8841b69319
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.

3.760 × 10⁹⁵(96-digit number)
37608851072661248007…07209935913306357759
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
3.760 × 10⁹⁵(96-digit number)
37608851072661248007…07209935913306357759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.521 × 10⁹⁵(96-digit number)
75217702145322496015…14419871826612715519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.504 × 10⁹⁶(97-digit number)
15043540429064499203…28839743653225431039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.008 × 10⁹⁶(97-digit number)
30087080858128998406…57679487306450862079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
6.017 × 10⁹⁶(97-digit number)
60174161716257996812…15358974612901724159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.203 × 10⁹⁷(98-digit number)
12034832343251599362…30717949225803448319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.406 × 10⁹⁷(98-digit number)
24069664686503198724…61435898451606896639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.813 × 10⁹⁷(98-digit number)
48139329373006397449…22871796903213793279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
9.627 × 10⁹⁷(98-digit number)
96278658746012794899…45743593806427586559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.925 × 10⁹⁸(99-digit number)
19255731749202558979…91487187612855173119
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:57,844,267 XPM·at block #6,825,022 · updates every 60s
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