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Block #75,910

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/21/2013, 7:59:34 PM Β· Difficulty 9.0525 Β· 6,719,598 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e03db532b2d83a7f80562b89d60d6b5ddbf143dec6459224877d8b2963f181ff
View on Chainz β†—

Height

#75,910

Difficulty

9.052466

Transactions

1

Size

198 B

Version

2

Bits

090d6e62

Nonce

35

Timestamp

7/21/2013, 7:59:34 PM

Confirmations

6,719,598

Merkle Root

d04d3e14da95a2f2ac05edb43e9d2117c0d05146160b61bc9fe74900c94c5d0b
Transactions (1)
Coinbased04d3e14da95a2…e74900c94c5d0b
1 in β†’ 1 out12.1900 XPM110 B
AbVtpxjx…2JADDKDE
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.

8.838 Γ— 10⁸⁸(89-digit number)
88386199512453970810…66135575744771116900
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
8.838 Γ— 10⁸⁸(89-digit number)
88386199512453970810…66135575744771116901
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.767 Γ— 10⁸⁹(90-digit number)
17677239902490794162…32271151489542233801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.535 Γ— 10⁸⁹(90-digit number)
35354479804981588324…64542302979084467601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.070 Γ— 10⁸⁹(90-digit number)
70708959609963176648…29084605958168935201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.414 Γ— 10⁹⁰(91-digit number)
14141791921992635329…58169211916337870401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.828 Γ— 10⁹⁰(91-digit number)
28283583843985270659…16338423832675740801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.656 Γ— 10⁹⁰(91-digit number)
56567167687970541318…32676847665351481601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.131 Γ— 10⁹¹(92-digit number)
11313433537594108263…65353695330702963201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.262 Γ— 10⁹¹(92-digit number)
22626867075188216527…30707390661405926401
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.

View full Prime Chain Discovery page β†’
β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9
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, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 75910

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock e03db532b2d83a7f80562b89d60d6b5ddbf143dec6459224877d8b2963f181ff

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #75,910 on Chainz β†—
Circulating Supply:57,608,129 XPMΒ·at block #6,795,507 Β· updates every 60s
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