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Block #1,721,283

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/17/2016, 11:35:02 AM Β· Difficulty 10.6777 Β· 5,088,984 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bbfa1f102e6ad8dcdf03020d4b530d3a132a068dd98d5175810dca4f73a54595
View on Chainz β†—

Height

#1,721,283

Difficulty

10.677687

Transactions

1

Size

243 B

Version

2

Bits

0aad7ce7

Nonce

155,171,144

Timestamp

8/17/2016, 11:35:02 AM

Confirmations

5,088,984

Mined by

⛏️ P2SHAKjaKd2Kxt1buNBYuJDadjFL1cDPsqUE8e

Merkle Root

325b90e81d029e341ec787435493ae647fd686b73c1223cd248df8988289a035
Transactions (1)
Coinbase325b90e81d029e…8df8988289a035
1 in β†’ 2 out8.7600 XPM152 B
AKjaKd2K…DPsqUE8eAXbk7f7A…Tx7JECPG
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.

3.533 Γ— 10⁹⁢(97-digit number)
35336781242216404894…64414953542187556481
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
3.533 Γ— 10⁹⁢(97-digit number)
35336781242216404894…64414953542187556481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.067 Γ— 10⁹⁢(97-digit number)
70673562484432809788…28829907084375112961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.413 Γ— 10⁹⁷(98-digit number)
14134712496886561957…57659814168750225921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.826 Γ— 10⁹⁷(98-digit number)
28269424993773123915…15319628337500451841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.653 Γ— 10⁹⁷(98-digit number)
56538849987546247830…30639256675000903681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.130 Γ— 10⁹⁸(99-digit number)
11307769997509249566…61278513350001807361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.261 Γ— 10⁹⁸(99-digit number)
22615539995018499132…22557026700003614721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.523 Γ— 10⁹⁸(99-digit number)
45231079990036998264…45114053400007229441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.046 Γ— 10⁹⁸(99-digit number)
90462159980073996529…90228106800014458881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.809 Γ— 10⁹⁹(100-digit number)
18092431996014799305…80456213600028917761
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:57,726,210 XPMΒ·at block #6,810,266 Β· updates every 60s
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