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Block #197,816

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/7/2013, 8:36:28 AM Β· Difficulty 9.8842 Β· 6,611,973 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
48196790ad01daac53f9682d146763035f1b9a10afe86b70b23abca46fd98ae2
View on Chainz β†—

Height

#197,816

Difficulty

9.884226

Transactions

2

Size

391 B

Version

2

Bits

09e25ca2

Nonce

20,585

Timestamp

10/7/2013, 8:36:28 AM

Confirmations

6,611,973

Mined by

⛏️ P2SHAU8CGpN3oep2LEHFtSY2YWudCx8dr4eLZa

Merkle Root

51376a5a5625c21493ca01a3a72898caad2ae6a92ea216a51a32a31646ce6c94
Transactions (2)
Coinbasecebbee60fe74af…b31da880995e8b
1 in β†’ 1 out10.2300 XPM109 B
AU8CGpN3…8dr4eLZa
45350600c2023e…4c6c267115683c
1 in β†’ 2 out10.2500 XPM192 B
AJfQWJkw…U9BcDBagAUKWcY89…NzCW79Af
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.

3.271 Γ— 10⁹⁴(95-digit number)
32716285333103940999…24272408288816988161
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
3.271 Γ— 10⁹⁴(95-digit number)
32716285333103940999…24272408288816988161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.543 Γ— 10⁹⁴(95-digit number)
65432570666207881999…48544816577633976321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.308 Γ— 10⁹⁡(96-digit number)
13086514133241576399…97089633155267952641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.617 Γ— 10⁹⁡(96-digit number)
26173028266483152799…94179266310535905281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.234 Γ— 10⁹⁡(96-digit number)
52346056532966305599…88358532621071810561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.046 Γ— 10⁹⁢(97-digit number)
10469211306593261119…76717065242143621121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.093 Γ— 10⁹⁢(97-digit number)
20938422613186522239…53434130484287242241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.187 Γ— 10⁹⁢(97-digit number)
41876845226373044479…06868260968574484481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.375 Γ— 10⁹⁢(97-digit number)
83753690452746088959…13736521937148968961
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,722,393 XPMΒ·at block #6,809,788 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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