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Block #268,907

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/22/2013, 1:30:24 PM Β· Difficulty 9.9560 Β· 6,540,337 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
88373c4b6f3ff0ad93c13bedcbe7e6d0a4ce6ea23e26282f6052816e9b453bf5
View on Chainz β†—

Height

#268,907

Difficulty

9.955998

Transactions

2

Size

723 B

Version

2

Bits

09f4bc49

Nonce

59,506

Timestamp

11/22/2013, 1:30:24 PM

Confirmations

6,540,337

Mined by

⛏️ P2SHAQd83bR5tTcjXKXTyt4v8joMKC83AUEb1s

Merkle Root

fb44bae1c69fe0745a06dcf68e28d417d8fee45301122a3bc6a3a5f5fc47c3db
Transactions (2)
Coinbaseb903e0ee3a3c32…6d0c60b547d190
1 in β†’ 1 out10.0800 XPM109 B
AQd83bR5…83AUEb1s
144cd6deabcc95…4c06975c6315f1
3 in β†’ 2 out365.0500 XPM524 B
Ac7RAQMV…nKWU2GLUAH3FHmHS…6yto1isQ
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.

4.901 Γ— 10⁹³(94-digit number)
49019437492912403680…46552190618799880961
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
4.901 Γ— 10⁹³(94-digit number)
49019437492912403680…46552190618799880961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.803 Γ— 10⁹³(94-digit number)
98038874985824807361…93104381237599761921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.960 Γ— 10⁹⁴(95-digit number)
19607774997164961472…86208762475199523841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.921 Γ— 10⁹⁴(95-digit number)
39215549994329922944…72417524950399047681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.843 Γ— 10⁹⁴(95-digit number)
78431099988659845889…44835049900798095361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.568 Γ— 10⁹⁡(96-digit number)
15686219997731969177…89670099801596190721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.137 Γ— 10⁹⁡(96-digit number)
31372439995463938355…79340199603192381441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.274 Γ— 10⁹⁡(96-digit number)
62744879990927876711…58680399206384762881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.254 Γ— 10⁹⁢(97-digit number)
12548975998185575342…17360798412769525761
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:57,718,018 XPMΒ·at block #6,809,243 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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