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Block #2,854,673

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/25/2018, 2:56:24 PM Β· Difficulty 11.7063 Β· 3,990,140 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
df287a40fc6c0c2c059e8ed47923cade796f353193789d2b0e6eea49fbab9fd2
View on Chainz β†—

Height

#2,854,673

Difficulty

11.706265

Transactions

2

Size

426 B

Version

2

Bits

0bb4cdc8

Nonce

1,140,270,738

Timestamp

9/25/2018, 2:56:24 PM

Confirmations

3,990,140

Mined by

⛏️ P2SHAREGWdvU6uaziAQdNwcZvjd3q46Dc949XP

Merkle Root

11d1019d57959d73037f1b1573c93a8808964d04f5cab0839319e8806c23477f
Transactions (2)
Coinbase90937c95dbe6ca…88948fe886588a
1 in β†’ 1 out7.3000 XPM110 B
AREGWdvU…6Dc949XP
050d6019ebaa5d…4d79c891e5bb62
1 in β†’ 2 out1320.7140 XPM226 B
AUwoKBLH…wMvQW8KcAHTR9Cpn…gA1xiEsW
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.

4.558 Γ— 10⁹⁴(95-digit number)
45587201693791110891…81810557010856876321
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
4.558 Γ— 10⁹⁴(95-digit number)
45587201693791110891…81810557010856876321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.117 Γ— 10⁹⁴(95-digit number)
91174403387582221782…63621114021713752641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.823 Γ— 10⁹⁡(96-digit number)
18234880677516444356…27242228043427505281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.646 Γ— 10⁹⁡(96-digit number)
36469761355032888712…54484456086855010561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.293 Γ— 10⁹⁡(96-digit number)
72939522710065777425…08968912173710021121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.458 Γ— 10⁹⁢(97-digit number)
14587904542013155485…17937824347420042241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.917 Γ— 10⁹⁢(97-digit number)
29175809084026310970…35875648694840084481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.835 Γ— 10⁹⁢(97-digit number)
58351618168052621940…71751297389680168961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.167 Γ— 10⁹⁷(98-digit number)
11670323633610524388…43502594779360337921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.334 Γ— 10⁹⁷(98-digit number)
23340647267221048776…87005189558720675841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.668 Γ— 10⁹⁷(98-digit number)
46681294534442097552…74010379117441351681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
9.336 Γ— 10⁹⁷(98-digit number)
93362589068884195104…48020758234882703361
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:58,002,911 XPMΒ·at block #6,844,812 Β· updates every 60s
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