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Block #136,096

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/27/2013, 12:31:09 AM Β· Difficulty 9.8144 Β· 6,673,840 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e466efb4511554153d11b391d5c8dbe63e7b7b625116b5fc21a67b1b09818bf5
View on Chainz β†—

Height

#136,096

Difficulty

9.814431

Transactions

1

Size

199 B

Version

2

Bits

09d07e8f

Nonce

158,571

Timestamp

8/27/2013, 12:31:09 AM

Confirmations

6,673,840

Mined by

⛏️ P2SHAcecj4WYP2kTRjXJMUTPed41WTwKtCNbS5

Merkle Root

6adee391f12463992225eff2c14dee9247669f95278d6a7d5b5817ef1aa00275
Transactions (1)
Coinbase6adee391f12463…5817ef1aa00275
1 in β†’ 1 out10.3700 XPM109 B
Acecj4WY…wKtCNbS5
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.

1.216 Γ— 10⁹⁡(96-digit number)
12166099464647700822…74162708061830236161
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
1.216 Γ— 10⁹⁡(96-digit number)
12166099464647700822…74162708061830236161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.433 Γ— 10⁹⁡(96-digit number)
24332198929295401645…48325416123660472321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.866 Γ— 10⁹⁡(96-digit number)
48664397858590803290…96650832247320944641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.732 Γ— 10⁹⁡(96-digit number)
97328795717181606581…93301664494641889281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.946 Γ— 10⁹⁢(97-digit number)
19465759143436321316…86603328989283778561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.893 Γ— 10⁹⁢(97-digit number)
38931518286872642632…73206657978567557121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.786 Γ— 10⁹⁢(97-digit number)
77863036573745285265…46413315957135114241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.557 Γ— 10⁹⁷(98-digit number)
15572607314749057053…92826631914270228481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.114 Γ— 10⁹⁷(98-digit number)
31145214629498114106…85653263828540456961
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:57,723,575 XPMΒ·at block #6,809,935 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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