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Block #1,610,743

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/2/2016, 8:56:38 AM Β· Difficulty 10.6060 Β· 5,234,283 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3bb56f163e395b9139dfda9ec4ff6f402c671125b30280c997d6d1f0268e781d
View on Chainz β†—

Height

#1,610,743

Difficulty

10.605983

Transactions

1

Size

198 B

Version

2

Bits

0a9b21ad

Nonce

723,365,945

Timestamp

6/2/2016, 8:56:38 AM

Confirmations

5,234,283

Mined by

⛏️ P2SHAUEyLYvZQdZgwDZUY5bbPRRE9qELYVpevC

Merkle Root

85ac0149ec9497c2a1c8353784f8ec3c487868b1538e258fd54b93763b8ea6fc
Transactions (1)
Coinbase85ac0149ec9497…4b93763b8ea6fc
1 in β†’ 1 out8.8800 XPM109 B
AUEyLYvZ…ELYVpevC
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.

1.392 Γ— 10⁹³(94-digit number)
13921095318778279866…56032149289613299201
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
1.392 Γ— 10⁹³(94-digit number)
13921095318778279866…56032149289613299201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.784 Γ— 10⁹³(94-digit number)
27842190637556559732…12064298579226598401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.568 Γ— 10⁹³(94-digit number)
55684381275113119464…24128597158453196801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.113 Γ— 10⁹⁴(95-digit number)
11136876255022623892…48257194316906393601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.227 Γ— 10⁹⁴(95-digit number)
22273752510045247785…96514388633812787201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.454 Γ— 10⁹⁴(95-digit number)
44547505020090495571…93028777267625574401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.909 Γ— 10⁹⁴(95-digit number)
89095010040180991142…86057554535251148801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.781 Γ— 10⁹⁡(96-digit number)
17819002008036198228…72115109070502297601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.563 Γ— 10⁹⁡(96-digit number)
35638004016072396456…44230218141004595201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.127 Γ— 10⁹⁡(96-digit number)
71276008032144792913…88460436282009190401
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:58,004,633 XPMΒ·at block #6,845,025 Β· updates every 60s
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