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Block #2,936,391

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/23/2018, 10:45:11 PM Β· Difficulty 11.3909 Β· 3,906,533 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e8d17cb856f1e7afd59803c64c4a255e7ca747bc259b5091b314ffa6c9211618
View on Chainz β†—

Height

#2,936,391

Difficulty

11.390856

Transactions

1

Size

200 B

Version

2

Bits

0b640f1c

Nonce

833,044,415

Timestamp

11/23/2018, 10:45:11 PM

Confirmations

3,906,533

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

9a0e582f6ec4017476ff07240da2df9c62e22cb7c5b8bc6225412cd116be2ded
Transactions (1)
Coinbase9a0e582f6ec401…412cd116be2ded
1 in β†’ 1 out7.6900 XPM110 B
AbXwmGxD…4XXYP765
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.

7.966 Γ— 10⁹³(94-digit number)
79665320645525191672…05046873098506776001
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
7.966 Γ— 10⁹³(94-digit number)
79665320645525191672…05046873098506776001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.593 Γ— 10⁹⁴(95-digit number)
15933064129105038334…10093746197013552001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.186 Γ— 10⁹⁴(95-digit number)
31866128258210076669…20187492394027104001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.373 Γ— 10⁹⁴(95-digit number)
63732256516420153338…40374984788054208001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.274 Γ— 10⁹⁡(96-digit number)
12746451303284030667…80749969576108416001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.549 Γ— 10⁹⁡(96-digit number)
25492902606568061335…61499939152216832001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.098 Γ— 10⁹⁡(96-digit number)
50985805213136122670…22999878304433664001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.019 Γ— 10⁹⁢(97-digit number)
10197161042627224534…45999756608867328001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.039 Γ— 10⁹⁢(97-digit number)
20394322085254449068…91999513217734656001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.078 Γ— 10⁹⁢(97-digit number)
40788644170508898136…83999026435469312001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.157 Γ— 10⁹⁢(97-digit number)
81577288341017796272…67998052870938624001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
1.631 Γ— 10⁹⁷(98-digit number)
16315457668203559254…35996105741877248001
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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