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Block #263,340

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/17/2013, 5:24:18 PM Β· Difficulty 9.9665 Β· 6,563,703 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ecd2b7f7ed89e9ca752625f94b36bc813bda63b672fb7908db180c1a4a855a45
View on Chainz β†—

Height

#263,340

Difficulty

9.966481

Transactions

1

Size

226 B

Version

2

Bits

09f76b48

Nonce

52,162

Timestamp

11/17/2013, 5:24:18 PM

Confirmations

6,563,703

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

5831fdf398ef0926e624bad5422c0e983524ed07075b0236f4e9f3ccf3b9749f
Transactions (1)
Coinbase5831fdf398ef09…e9f3ccf3b9749f
1 in β†’ 2 out10.0500 XPM136 B
AKcbk49N…GJbKa7j1AHsw4d6U…EnM8UXNZ
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.

9.020 Γ— 10⁹⁴(95-digit number)
90203974971544452862…96554315478274195001
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
9.020 Γ— 10⁹⁴(95-digit number)
90203974971544452862…96554315478274195001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.804 Γ— 10⁹⁡(96-digit number)
18040794994308890572…93108630956548390001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.608 Γ— 10⁹⁡(96-digit number)
36081589988617781145…86217261913096780001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.216 Γ— 10⁹⁡(96-digit number)
72163179977235562290…72434523826193560001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.443 Γ— 10⁹⁢(97-digit number)
14432635995447112458…44869047652387120001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.886 Γ— 10⁹⁢(97-digit number)
28865271990894224916…89738095304774240001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.773 Γ— 10⁹⁢(97-digit number)
57730543981788449832…79476190609548480001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.154 Γ— 10⁹⁷(98-digit number)
11546108796357689966…58952381219096960001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.309 Γ— 10⁹⁷(98-digit number)
23092217592715379932…17904762438193920001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.618 Γ— 10⁹⁷(98-digit number)
46184435185430759865…35809524876387840001
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:57,860,525 XPMΒ·at block #6,827,042 Β· updates every 60s
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