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Block #2,190,359

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/3/2017, 2:02:34 AM Β· Difficulty 10.9495 Β· 4,652,903 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
06c2ed0e5128a15b542a9280756cf5448b23fc56fe55ea3e28e61875626c5914
View on Chainz β†—

Height

#2,190,359

Difficulty

10.949527

Transactions

2

Size

575 B

Version

2

Bits

0af31438

Nonce

1,074,495,086

Timestamp

7/3/2017, 2:02:34 AM

Confirmations

4,652,903

Mined by

⛏️ P2SHAThpcdrRx4ZW25oys8qrQEKuXj6qmXUY55

Merkle Root

6b9af12590caa59c19a913692e0fc54fed3a00b9e07dc73c8dcaa9032e71447a
Transactions (2)
Coinbasecff555117ce597…438baef4ee7bbd
1 in β†’ 1 out8.3400 XPM110 B
AThpcdrR…6qmXUY55
7792c2469cece0…8821495fe231db
2 in β†’ 2 out1000.0002 XPM375 B
AaTmXD5N…UpWpd7woAWktA8iw…W9tnxqP8
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.583 Γ— 10⁹⁡(96-digit number)
55833271464944759893…43348602934458009601
Discovered Prime Numbers
p_k = 2^k Γ— 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
5.583 Γ— 10⁹⁡(96-digit number)
55833271464944759893…43348602934458009601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.116 Γ— 10⁹⁢(97-digit number)
11166654292988951978…86697205868916019201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.233 Γ— 10⁹⁢(97-digit number)
22333308585977903957…73394411737832038401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.466 Γ— 10⁹⁢(97-digit number)
44666617171955807914…46788823475664076801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.933 Γ— 10⁹⁢(97-digit number)
89333234343911615828…93577646951328153601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.786 Γ— 10⁹⁷(98-digit number)
17866646868782323165…87155293902656307201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.573 Γ— 10⁹⁷(98-digit number)
35733293737564646331…74310587805312614401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.146 Γ— 10⁹⁷(98-digit number)
71466587475129292663…48621175610625228801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.429 Γ— 10⁹⁸(99-digit number)
14293317495025858532…97242351221250457601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.858 Γ— 10⁹⁸(99-digit number)
28586634990051717065…94484702442500915201
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,990,469 XPMΒ·at block #6,843,261 Β· updates every 60s
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