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Block #233,880

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/29/2013, 11:55:51 PM Β· Difficulty 9.9432 Β· 6,572,862 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
910679cabec7a85a785383dfa417673d8ac452e9b3d088e1ec42963d6ef98cf9
View on Chainz β†—

Height

#233,880

Difficulty

9.943240

Transactions

2

Size

394 B

Version

2

Bits

09f17833

Nonce

169,331

Timestamp

10/29/2013, 11:55:51 PM

Confirmations

6,572,862

Mined by

⛏️ P2SHASz4Fhr87XRfquDbLrVuuGbuM7AwU53GGj

Merkle Root

90457af172b2cf1f3e17b7aafcef1b1736fb4244d43f5819370c8c22860212d7
Transactions (2)
Coinbase0eec028aa913da…87483506419517
1 in β†’ 1 out10.1100 XPM109 B
ASz4Fhr8…AwU53GGj
8cf46bd692d749…6c372ee8533b24
1 in β†’ 1 out10.0623 XPM193 B
AW9FEVK5…L9RUzGJM
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.

2.541 Γ— 10⁹⁸(99-digit number)
25413874897298360382…99445029238402961921
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
2.541 Γ— 10⁹⁸(99-digit number)
25413874897298360382…99445029238402961921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.082 Γ— 10⁹⁸(99-digit number)
50827749794596720764…98890058476805923841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.016 Γ— 10⁹⁹(100-digit number)
10165549958919344152…97780116953611847681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.033 Γ— 10⁹⁹(100-digit number)
20331099917838688305…95560233907223695361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.066 Γ— 10⁹⁹(100-digit number)
40662199835677376611…91120467814447390721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.132 Γ— 10⁹⁹(100-digit number)
81324399671354753223…82240935628894781441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.626 Γ— 10¹⁰⁰(101-digit number)
16264879934270950644…64481871257789562881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.252 Γ— 10¹⁰⁰(101-digit number)
32529759868541901289…28963742515579125761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.505 Γ— 10¹⁰⁰(101-digit number)
65059519737083802578…57927485031158251521
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:57,698,033 XPMΒ·at block #6,806,741 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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