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Block #2,645,582

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/2/2018, 11:34:20 PM Β· Difficulty 11.7349 Β· 4,193,885 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6548b93beda1d443db9a4f9c3be4e00ae35643ca05f3232a16ce1c2626bcf585
View on Chainz β†—

Height

#2,645,582

Difficulty

11.734862

Transactions

1

Size

200 B

Version

2

Bits

0bbc1ff2

Nonce

138,268,359

Timestamp

5/2/2018, 11:34:20 PM

Confirmations

4,193,885

Mined by

⛏️ P2SHAeS7RqN4B5CqPBi5wLxbgQKfheiVSkBoWk

Merkle Root

ae53becd2c8f2d2b4140a8400cf1cb832a3fea0ebff35d98ba68c4faa065cdb2
Transactions (1)
Coinbaseae53becd2c8f2d…68c4faa065cdb2
1 in β†’ 1 out7.2500 XPM110 B
AeS7RqN4…iVSkBoWk
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.

6.770 Γ— 10⁹⁴(95-digit number)
67706505953655235423…91594181680040903681
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
6.770 Γ— 10⁹⁴(95-digit number)
67706505953655235423…91594181680040903681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.354 Γ— 10⁹⁡(96-digit number)
13541301190731047084…83188363360081807361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.708 Γ— 10⁹⁡(96-digit number)
27082602381462094169…66376726720163614721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.416 Γ— 10⁹⁡(96-digit number)
54165204762924188338…32753453440327229441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.083 Γ— 10⁹⁢(97-digit number)
10833040952584837667…65506906880654458881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.166 Γ— 10⁹⁢(97-digit number)
21666081905169675335…31013813761308917761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.333 Γ— 10⁹⁢(97-digit number)
43332163810339350671…62027627522617835521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.666 Γ— 10⁹⁢(97-digit number)
86664327620678701342…24055255045235671041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.733 Γ— 10⁹⁷(98-digit number)
17332865524135740268…48110510090471342081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.466 Γ— 10⁹⁷(98-digit number)
34665731048271480536…96221020180942684161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.933 Γ— 10⁹⁷(98-digit number)
69331462096542961073…92442040361885368321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
1.386 Γ— 10⁹⁸(99-digit number)
13866292419308592214…84884080723770736641
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,960,027 XPMΒ·at block #6,839,466 Β· updates every 60s
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