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Block #1,723,420

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/18/2016, 8:45:45 PM Β· Difficulty 10.6869 Β· 5,094,265 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a8c31428851fe826437b760ff1cc5cee23df449d9dbd7b6fa8836cd24968561a
View on Chainz β†—

Height

#1,723,420

Difficulty

10.686854

Transactions

1

Size

200 B

Version

2

Bits

0aafd5b0

Nonce

529,843,809

Timestamp

8/18/2016, 8:45:45 PM

Confirmations

5,094,265

Mined by

⛏️ P2SHAKPP5CpS6anexDc3NfpYjwPHU9naPAeoDR

Merkle Root

bceb53d2e7160e77dd9cd740cacbb9e728ed092fb84b11a2e5e6e872f58ba178
Transactions (1)
Coinbasebceb53d2e7160e…e6e872f58ba178
1 in β†’ 1 out8.7400 XPM110 B
AKPP5CpS…naPAeoDR
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.

1.509 Γ— 10⁹⁡(96-digit number)
15092396556427745105…99267194500642358801
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
1.509 Γ— 10⁹⁡(96-digit number)
15092396556427745105…99267194500642358801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.018 Γ— 10⁹⁡(96-digit number)
30184793112855490210…98534389001284717601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.036 Γ— 10⁹⁡(96-digit number)
60369586225710980421…97068778002569435201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.207 Γ— 10⁹⁢(97-digit number)
12073917245142196084…94137556005138870401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.414 Γ— 10⁹⁢(97-digit number)
24147834490284392168…88275112010277740801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.829 Γ— 10⁹⁢(97-digit number)
48295668980568784337…76550224020555481601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.659 Γ— 10⁹⁢(97-digit number)
96591337961137568674…53100448041110963201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.931 Γ— 10⁹⁷(98-digit number)
19318267592227513734…06200896082221926401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.863 Γ— 10⁹⁷(98-digit number)
38636535184455027469…12401792164443852801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.727 Γ— 10⁹⁷(98-digit number)
77273070368910054939…24803584328887705601
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:57,785,538 XPMΒ·at block #6,817,684 Β· updates every 60s
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