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Block #46,389

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/15/2013, 6:21:13 AM Β· Difficulty 8.7905 Β· 6,766,073 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2fa9431e4ddad472e8e855544ddddf6b95d9ce13d47cdcf953eb22a27c366d67
View on Chainz β†—

Height

#46,389

Difficulty

8.790541

Transactions

2

Size

397 B

Version

2

Bits

08ca60df

Nonce

911

Timestamp

7/15/2013, 6:21:13 AM

Confirmations

6,766,073

Merkle Root

f72aa086eb062c3f224b42d8b2cf36750e2f392e4fec0030b2aa984dd99d01d8
Transactions (2)
Coinbase9679eb24263c09…54b3874c641de7
1 in β†’ 1 out12.9300 XPM110 B
AYMUqE8c…eb8kqZ2H
8b274f9d36fa17…3ad74f7da259f6
1 in β†’ 1 out12.9800 XPM192 B
AQi9roZv…a6NMn7Fp
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.

1.155 Γ— 10¹⁰⁷(108-digit number)
11551987628452513384…70483658970908016500
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
1.155 Γ— 10¹⁰⁷(108-digit number)
11551987628452513384…70483658970908016501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.310 Γ— 10¹⁰⁷(108-digit number)
23103975256905026769…40967317941816033001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.620 Γ— 10¹⁰⁷(108-digit number)
46207950513810053539…81934635883632066001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.241 Γ— 10¹⁰⁷(108-digit number)
92415901027620107079…63869271767264132001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.848 Γ— 10¹⁰⁸(109-digit number)
18483180205524021415…27738543534528264001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.696 Γ— 10¹⁰⁸(109-digit number)
36966360411048042831…55477087069056528001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.393 Γ— 10¹⁰⁸(109-digit number)
73932720822096085663…10954174138113056001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.478 Γ— 10¹⁰⁹(110-digit number)
14786544164419217132…21908348276226112001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8
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 46389

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 2fa9431e4ddad472e8e855544ddddf6b95d9ce13d47cdcf953eb22a27c366d67

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 #46,389 on Chainz β†—
Circulating Supply:57,743,722 XPMΒ·at block #6,812,461 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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