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Block #1,395,498

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/2/2016, 5:05:37 AM Β· Difficulty 10.8115 Β· 5,430,199 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7cd5cab221157711492c827753058fb5e9d99a2e01abfebdf43d4b7edc2622f2
View on Chainz β†—

Height

#1,395,498

Difficulty

10.811492

Transactions

1

Size

199 B

Version

2

Bits

0acfbdf6

Nonce

1,020,928,426

Timestamp

1/2/2016, 5:05:37 AM

Confirmations

5,430,199

Mined by

⛏️ P2SHAcmoYg566BzXJPAHmJvDrcxJ5Eor9HKeyK

Merkle Root

04fe0337353a9fec00a343d0653ccabddd4d9c0b2b5aa9c27a6530dab9906834
Transactions (1)
Coinbase04fe0337353a9f…6530dab9906834
1 in β†’ 1 out8.5400 XPM109 B
AcmoYg56…or9HKeyK
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.

3.963 Γ— 10⁹⁡(96-digit number)
39632679693327950058…11494983257233679361
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
3.963 Γ— 10⁹⁡(96-digit number)
39632679693327950058…11494983257233679361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.926 Γ— 10⁹⁡(96-digit number)
79265359386655900116…22989966514467358721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.585 Γ— 10⁹⁢(97-digit number)
15853071877331180023…45979933028934717441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.170 Γ— 10⁹⁢(97-digit number)
31706143754662360046…91959866057869434881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.341 Γ— 10⁹⁢(97-digit number)
63412287509324720093…83919732115738869761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.268 Γ— 10⁹⁷(98-digit number)
12682457501864944018…67839464231477739521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.536 Γ— 10⁹⁷(98-digit number)
25364915003729888037…35678928462955479041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.072 Γ— 10⁹⁷(98-digit number)
50729830007459776074…71357856925910958081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.014 Γ— 10⁹⁸(99-digit number)
10145966001491955214…42715713851821916161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.029 Γ— 10⁹⁸(99-digit number)
20291932002983910429…85431427703643832321
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,849,688 XPMΒ·at block #6,825,696 Β· updates every 60s
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