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Block #2,796,300

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/16/2018, 8:19:54 AM Β· Difficulty 11.6812 Β· 4,045,852 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6bd9ad4f2de8d3259801e2d8e4bdccb69f2a9f2c12706394be841b9a50c0f073
View on Chainz β†—

Height

#2,796,300

Difficulty

11.681208

Transactions

1

Size

200 B

Version

2

Bits

0bae63a1

Nonce

890,271,317

Timestamp

8/16/2018, 8:19:54 AM

Confirmations

4,045,852

Mined by

⛏️ P2SHAR3yzPjEVkrK32c2kTMYdWc8wHSQZPQm49

Merkle Root

e46b48bbab9a8a23fc5fd3b976f581e7cf4bcb09b5e44659e04e910015c9b5a8
Transactions (1)
Coinbasee46b48bbab9a8a…4e910015c9b5a8
1 in β†’ 1 out7.3200 XPM110 B
AR3yzPjE…SQZPQm49
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.

5.248 Γ— 10⁹⁡(96-digit number)
52489291059892342682…72043770664626513921
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
5.248 Γ— 10⁹⁡(96-digit number)
52489291059892342682…72043770664626513921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.049 Γ— 10⁹⁢(97-digit number)
10497858211978468536…44087541329253027841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.099 Γ— 10⁹⁢(97-digit number)
20995716423956937072…88175082658506055681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.199 Γ— 10⁹⁢(97-digit number)
41991432847913874145…76350165317012111361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.398 Γ— 10⁹⁢(97-digit number)
83982865695827748291…52700330634024222721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.679 Γ— 10⁹⁷(98-digit number)
16796573139165549658…05400661268048445441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.359 Γ— 10⁹⁷(98-digit number)
33593146278331099316…10801322536096890881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.718 Γ— 10⁹⁷(98-digit number)
67186292556662198633…21602645072193781761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.343 Γ— 10⁹⁸(99-digit number)
13437258511332439726…43205290144387563521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.687 Γ— 10⁹⁸(99-digit number)
26874517022664879453…86410580288775127041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.374 Γ— 10⁹⁸(99-digit number)
53749034045329758906…72821160577550254081
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:57,981,605 XPMΒ·at block #6,842,151 Β· updates every 60s
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