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Block #2,849,476

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/21/2018, 4:45:57 PM Β· Difficulty 11.7313 Β· 3,990,685 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bf8b382f78f47648149afd551cfbd1681f4a7037bf3c731922eb9d17e621d2e0
View on Chainz β†—

Height

#2,849,476

Difficulty

11.731257

Transactions

2

Size

4.18 KB

Version

2

Bits

0bbb33a8

Nonce

1,704,168,647

Timestamp

9/21/2018, 4:45:57 PM

Confirmations

3,990,685

Mined by

⛏️ P2SHALgaMHt7hH1v3iDzEcBHeHRRNqZGLaNmmT

Merkle Root

5de8ca73fac10fb53a55cbdfdfd6ebec0face572fd16c018ffd56d9f55f214ac
Transactions (2)
Coinbased71a20362f9940…73c93f4dffd7ad
1 in β†’ 1 out7.3000 XPM110 B
ALgaMHt7…ZGLaNmmT
87170c443bdf2b…d8f2040272b770
27 in β†’ 2 out260.5300 XPM3.98 KB
AQR4i2Fa…S4YuJG46ALh5G3Np…6TsNC2wj
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.

6.458 Γ— 10⁹⁢(97-digit number)
64588039867057222595…18431770758344929281
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
6.458 Γ— 10⁹⁢(97-digit number)
64588039867057222595…18431770758344929281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.291 Γ— 10⁹⁷(98-digit number)
12917607973411444519…36863541516689858561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.583 Γ— 10⁹⁷(98-digit number)
25835215946822889038…73727083033379717121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.167 Γ— 10⁹⁷(98-digit number)
51670431893645778076…47454166066759434241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.033 Γ— 10⁹⁸(99-digit number)
10334086378729155615…94908332133518868481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.066 Γ— 10⁹⁸(99-digit number)
20668172757458311230…89816664267037736961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.133 Γ— 10⁹⁸(99-digit number)
41336345514916622461…79633328534075473921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.267 Γ— 10⁹⁸(99-digit number)
82672691029833244922…59266657068150947841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.653 Γ— 10⁹⁹(100-digit number)
16534538205966648984…18533314136301895681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.306 Γ— 10⁹⁹(100-digit number)
33069076411933297969…37066628272603791361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.613 Γ— 10⁹⁹(100-digit number)
66138152823866595938…74133256545207582721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
1.322 Γ— 10¹⁰⁰(101-digit number)
13227630564773319187…48266513090415165441
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
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