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Block #266,752

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/20/2013, 4:57:05 PM Β· Difficulty 9.9602 Β· 6,542,363 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1eaa8006451dfec2c39450ce9d5d44e96c1e6eccc19d7b69860e37048ae3fbd0
View on Chainz β†—

Height

#266,752

Difficulty

9.960221

Transactions

2

Size

575 B

Version

2

Bits

09f5d10c

Nonce

360,331

Timestamp

11/20/2013, 4:57:05 PM

Confirmations

6,542,363

Mined by

⛏️ P2SHAGNPrf4Wya2PSBnXmVeYxGwKdBu7DkzwQ8

Merkle Root

e3f914bf12b8ce00c3ff20c7041575590345c2eeab81409f6a0dca4d5b5fe946
Transactions (2)
Coinbase3c5534ed9bd041…d5e9e661466860
1 in β†’ 1 out10.0700 XPM109 B
AGNPrf4W…u7DkzwQ8
7e08c212e52c01…b68a094d6ca5d4
2 in β†’ 2 out27.7809 XPM375 B
Ac9RjjXq…8j4UBEJYAbsTko5Q…Dwd7UBRU
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.

5.342 Γ— 10⁹⁢(97-digit number)
53421990893736830642…00075908390632960001
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
5.342 Γ— 10⁹⁢(97-digit number)
53421990893736830642…00075908390632960001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.068 Γ— 10⁹⁷(98-digit number)
10684398178747366128…00151816781265920001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.136 Γ— 10⁹⁷(98-digit number)
21368796357494732257…00303633562531840001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.273 Γ— 10⁹⁷(98-digit number)
42737592714989464514…00607267125063680001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.547 Γ— 10⁹⁷(98-digit number)
85475185429978929028…01214534250127360001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.709 Γ— 10⁹⁸(99-digit number)
17095037085995785805…02429068500254720001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.419 Γ— 10⁹⁸(99-digit number)
34190074171991571611…04858137000509440001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.838 Γ— 10⁹⁸(99-digit number)
68380148343983143222…09716274001018880001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.367 Γ— 10⁹⁹(100-digit number)
13676029668796628644…19432548002037760001
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:57,716,977 XPMΒ·at block #6,809,114 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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