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Block #269,392

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/23/2013, 2:29:01 AM Β· Difficulty 9.9534 Β· 6,539,435 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1ccc3cecf3736fb495c6736b4ce6a8dcd1a53f96f399ddd1ae09b6afd1322550
View on Chainz β†—

Height

#269,392

Difficulty

9.953373

Transactions

2

Size

835 B

Version

2

Bits

09f41039

Nonce

27,071

Timestamp

11/23/2013, 2:29:01 AM

Confirmations

6,539,435

Mined by

⛏️ P2SHAZgYtNSG5AreNkuRBWQhbqCMyJdpr1Hcz2

Merkle Root

ffa57053e5e7cf78972dbc829716886f84885f5d49e38d3b8c9576eae0676530
Transactions (2)
Coinbasea7bb41f0fad4d0…2c71c6a635703e
1 in β†’ 1 out10.0900 XPM109 B
AZgYtNSG…dpr1Hcz2
da5a4d4596ec76…e687feaea89cfe
4 in β†’ 1 out9.1222 XPM636 B
Ab2EJo7A…GbDZf26e
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.

3.910 Γ— 10⁹³(94-digit number)
39103776474499360734…76971698266976251381
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
3.910 Γ— 10⁹³(94-digit number)
39103776474499360734…76971698266976251381
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.820 Γ— 10⁹³(94-digit number)
78207552948998721468…53943396533952502761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.564 Γ— 10⁹⁴(95-digit number)
15641510589799744293…07886793067905005521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.128 Γ— 10⁹⁴(95-digit number)
31283021179599488587…15773586135810011041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.256 Γ— 10⁹⁴(95-digit number)
62566042359198977174…31547172271620022081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.251 Γ— 10⁹⁡(96-digit number)
12513208471839795434…63094344543240044161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.502 Γ— 10⁹⁡(96-digit number)
25026416943679590869…26188689086480088321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.005 Γ— 10⁹⁡(96-digit number)
50052833887359181739…52377378172960176641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.001 Γ— 10⁹⁢(97-digit number)
10010566777471836347…04754756345920353281
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:57,714,674 XPMΒ·at block #6,808,826 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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