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Block #75,588

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/21/2013, 5:28:35 PM Β· Difficulty 9.0196 Β· 6,731,252 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3206dc16cbaf374595a21310b575e56e58ee9b909dcf6c4ba15fec7550bf1ac8
View on Chainz β†—

Height

#75,588

Difficulty

9.019624

Transactions

1

Size

205 B

Version

2

Bits

0905060c

Nonce

603

Timestamp

7/21/2013, 5:28:35 PM

Confirmations

6,731,252

Mined by

⛏️ P2SHAKZxB9sLnFagacwoGg9Nd9LCvLZhxs5zB5

Merkle Root

bd21587b9123a6036c68b049f8065dc00ba4eb80d891403e6dc713a132f95842
Transactions (1)
Coinbasebd21587b9123a6…c713a132f95842
1 in β†’ 1 out12.2700 XPM110 B
AKZxB9sL…Zhxs5zB5
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.

1.365 Γ— 10¹⁰⁷(108-digit number)
13652427738355329638…40258718186171098501
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
1.365 Γ— 10¹⁰⁷(108-digit number)
13652427738355329638…40258718186171098501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.730 Γ— 10¹⁰⁷(108-digit number)
27304855476710659276…80517436372342197001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.460 Γ— 10¹⁰⁷(108-digit number)
54609710953421318552…61034872744684394001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.092 Γ— 10¹⁰⁸(109-digit number)
10921942190684263710…22069745489368788001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.184 Γ— 10¹⁰⁸(109-digit number)
21843884381368527421…44139490978737576001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.368 Γ— 10¹⁰⁸(109-digit number)
43687768762737054842…88278981957475152001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.737 Γ— 10¹⁰⁸(109-digit number)
87375537525474109684…76557963914950304001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.747 Γ— 10¹⁰⁹(110-digit number)
17475107505094821936…53115927829900608001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.495 Γ— 10¹⁰⁹(110-digit number)
34950215010189643873…06231855659801216001
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:57,698,823 XPMΒ·at block #6,806,839 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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