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Block #2,773,297

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/31/2018, 1:31:15 PM Β· Difficulty 11.6627 Β· 4,071,142 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c90bafcdd3ef0befb9ae7977f1345cea14ae64daed5784e2e4924ea17ca193cd
View on Chainz β†—

Height

#2,773,297

Difficulty

11.662661

Transactions

1

Size

199 B

Version

2

Bits

0ba9a424

Nonce

547,061,167

Timestamp

7/31/2018, 1:31:15 PM

Confirmations

4,071,142

Mined by

⛏️ P2SHAc8GFLe5XyjD1JdDQ3L3mrT1uDNooh5EWE

Merkle Root

cfd6298c8b511af54dbcd8b87449c0435fbc74fd9ab92f06bff26d46bfd3af1e
Transactions (1)
Coinbasecfd6298c8b511a…f26d46bfd3af1e
1 in β†’ 1 out7.3400 XPM110 B
Ac8GFLe5…Nooh5EWE
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.

3.288 Γ— 10⁹³(94-digit number)
32889079413493200051…24676498315647127041
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
3.288 Γ— 10⁹³(94-digit number)
32889079413493200051…24676498315647127041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.577 Γ— 10⁹³(94-digit number)
65778158826986400103…49352996631294254081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.315 Γ— 10⁹⁴(95-digit number)
13155631765397280020…98705993262588508161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.631 Γ— 10⁹⁴(95-digit number)
26311263530794560041…97411986525177016321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.262 Γ— 10⁹⁴(95-digit number)
52622527061589120082…94823973050354032641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.052 Γ— 10⁹⁡(96-digit number)
10524505412317824016…89647946100708065281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.104 Γ— 10⁹⁡(96-digit number)
21049010824635648033…79295892201416130561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.209 Γ— 10⁹⁡(96-digit number)
42098021649271296066…58591784402832261121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.419 Γ— 10⁹⁡(96-digit number)
84196043298542592132…17183568805664522241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.683 Γ— 10⁹⁢(97-digit number)
16839208659708518426…34367137611329044481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.367 Γ— 10⁹⁢(97-digit number)
33678417319417036853…68734275222658088961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
6.735 Γ— 10⁹⁢(97-digit number)
67356834638834073706…37468550445316177921
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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