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Block #2,749,320

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/15/2018, 1:21:22 AM Β· Difficulty 11.6476 Β· 4,093,764 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f43cfa7a43610826d6f9e23981297208d241c340f093f731b60694b339ff2dff
View on Chainz β†—

Height

#2,749,320

Difficulty

11.647569

Transactions

1

Size

200 B

Version

2

Bits

0ba5c70e

Nonce

100,729,641

Timestamp

7/15/2018, 1:21:22 AM

Confirmations

4,093,764

Mined by

⛏️ P2SHAS4fz1HM5xgrx1xtwy3pMKX3XD98g6doDH

Merkle Root

ec0bd84abd8fb10c59ccf9cb12e25673a2a7a4b2c423de01f2d606be84ed4096
Transactions (1)
Coinbaseec0bd84abd8fb1…d606be84ed4096
1 in β†’ 1 out7.3600 XPM110 B
AS4fz1HM…98g6doDH
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.

6.264 Γ— 10⁹⁡(96-digit number)
62647172597385986873…52124162749558620801
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
6.264 Γ— 10⁹⁡(96-digit number)
62647172597385986873…52124162749558620801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.252 Γ— 10⁹⁢(97-digit number)
12529434519477197374…04248325499117241601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.505 Γ— 10⁹⁢(97-digit number)
25058869038954394749…08496650998234483201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.011 Γ— 10⁹⁢(97-digit number)
50117738077908789499…16993301996468966401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.002 Γ— 10⁹⁷(98-digit number)
10023547615581757899…33986603992937932801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.004 Γ— 10⁹⁷(98-digit number)
20047095231163515799…67973207985875865601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.009 Γ— 10⁹⁷(98-digit number)
40094190462327031599…35946415971751731201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.018 Γ— 10⁹⁷(98-digit number)
80188380924654063198…71892831943503462401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.603 Γ— 10⁹⁸(99-digit number)
16037676184930812639…43785663887006924801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.207 Γ— 10⁹⁸(99-digit number)
32075352369861625279…87571327774013849601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.415 Γ— 10⁹⁸(99-digit number)
64150704739723250558…75142655548027699201
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
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