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Block #2,847,430

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/20/2018, 6:04:44 AM Β· Difficulty 11.7330 Β· 3,993,355 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2b7b13542e6a1dbc855b2fbb4722663acda0ce5ce6170b9dee9db42038e0d5df
View on Chainz β†—

Height

#2,847,430

Difficulty

11.733050

Transactions

1

Size

201 B

Version

2

Bits

0bbba92a

Nonce

139,772,457

Timestamp

9/20/2018, 6:04:44 AM

Confirmations

3,993,355

Mined by

⛏️ P2SHAcdFiAdbf6w1JXRUzzc31WuLATrNcshpt3

Merkle Root

e61ebff8420421a8ae597fc6d05d9a2fa3171019cf1fd4c8157c8455b3f8a72a
Transactions (1)
Coinbasee61ebff8420421…7c8455b3f8a72a
1 in β†’ 1 out7.2500 XPM110 B
AcdFiAdb…rNcshpt3
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.

8.251 Γ— 10⁹⁡(96-digit number)
82514595978008729903…69184782550166535681
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
8.251 Γ— 10⁹⁡(96-digit number)
82514595978008729903…69184782550166535681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.650 Γ— 10⁹⁢(97-digit number)
16502919195601745980…38369565100333071361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.300 Γ— 10⁹⁢(97-digit number)
33005838391203491961…76739130200666142721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.601 Γ— 10⁹⁢(97-digit number)
66011676782406983923…53478260401332285441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.320 Γ— 10⁹⁷(98-digit number)
13202335356481396784…06956520802664570881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.640 Γ— 10⁹⁷(98-digit number)
26404670712962793569…13913041605329141761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.280 Γ— 10⁹⁷(98-digit number)
52809341425925587138…27826083210658283521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.056 Γ— 10⁹⁸(99-digit number)
10561868285185117427…55652166421316567041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.112 Γ— 10⁹⁸(99-digit number)
21123736570370234855…11304332842633134081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.224 Γ— 10⁹⁸(99-digit number)
42247473140740469710…22608665685266268161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.449 Γ— 10⁹⁸(99-digit number)
84494946281480939421…45217331370532536321
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,970,626 XPMΒ·at block #6,840,784 Β· updates every 60s
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