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Block #2,795,754

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/15/2018, 11:12:35 PM Β· Difficulty 11.6813 Β· 4,045,493 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9eeb1354753019261befdd432b52f683449967e8a2bdd324e51af687a26824e3
View on Chainz β†—

Height

#2,795,754

Difficulty

11.681296

Transactions

1

Size

199 B

Version

2

Bits

0bae6964

Nonce

1,996,937,093

Timestamp

8/15/2018, 11:12:35 PM

Confirmations

4,045,493

Mined by

⛏️ P2SHAUd5AszyzxZomkoyXNfW48cv9pKMruGg2M

Merkle Root

3ae3120fbf434108d96865af4098b5c6076e15990316f888528fdb7cd2df5136
Transactions (1)
Coinbase3ae3120fbf4341…8fdb7cd2df5136
1 in β†’ 1 out7.3200 XPM110 B
AUd5Aszy…KMruGg2M
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.

1.153 Γ— 10⁹³(94-digit number)
11539691887174973275…96366400007427739401
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
1.153 Γ— 10⁹³(94-digit number)
11539691887174973275…96366400007427739401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.307 Γ— 10⁹³(94-digit number)
23079383774349946551…92732800014855478801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.615 Γ— 10⁹³(94-digit number)
46158767548699893103…85465600029710957601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.231 Γ— 10⁹³(94-digit number)
92317535097399786206…70931200059421915201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.846 Γ— 10⁹⁴(95-digit number)
18463507019479957241…41862400118843830401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.692 Γ— 10⁹⁴(95-digit number)
36927014038959914482…83724800237687660801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.385 Γ— 10⁹⁴(95-digit number)
73854028077919828964…67449600475375321601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.477 Γ— 10⁹⁡(96-digit number)
14770805615583965792…34899200950750643201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.954 Γ— 10⁹⁡(96-digit number)
29541611231167931585…69798401901501286401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.908 Γ— 10⁹⁡(96-digit number)
59083222462335863171…39596803803002572801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.181 Γ— 10⁹⁢(97-digit number)
11816644492467172634…79193607606005145601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,974,338 XPMΒ·at block #6,841,246 Β· updates every 60s
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