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Block #280,934

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/28/2013, 8:42:01 PM Β· Difficulty 9.9758 Β· 6,528,642 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
34ffb5efa73ef9fd773131b6c96b436b48fa16ad9c339e90bd93f1e8a0cfaef6
View on Chainz β†—

Height

#280,934

Difficulty

9.975787

Transactions

1

Size

199 B

Version

2

Bits

09f9cd2e

Nonce

96,031

Timestamp

11/28/2013, 8:42:01 PM

Confirmations

6,528,642

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

d699c872e8d959a5dd88e612b90611165ebb79997440a2bff2f2389e9a225dc6
Transactions (1)
Coinbased699c872e8d959…f2389e9a225dc6
1 in β†’ 1 out10.0300 XPM110 B
AeKNrjNj…1NEq95Ta
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.

1.309 Γ— 10⁹³(94-digit number)
13097514007293321272…94353441139051572301
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
1.309 Γ— 10⁹³(94-digit number)
13097514007293321272…94353441139051572301
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.619 Γ— 10⁹³(94-digit number)
26195028014586642545…88706882278103144601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.239 Γ— 10⁹³(94-digit number)
52390056029173285090…77413764556206289201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.047 Γ— 10⁹⁴(95-digit number)
10478011205834657018…54827529112412578401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.095 Γ— 10⁹⁴(95-digit number)
20956022411669314036…09655058224825156801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.191 Γ— 10⁹⁴(95-digit number)
41912044823338628072…19310116449650313601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.382 Γ— 10⁹⁴(95-digit number)
83824089646677256145…38620232899300627201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.676 Γ— 10⁹⁡(96-digit number)
16764817929335451229…77240465798601254401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.352 Γ— 10⁹⁡(96-digit number)
33529635858670902458…54480931597202508801
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:57,720,685 XPMΒ·at block #6,809,575 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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