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Home/Chain Registry/Block #146,541

Block #146,541

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/2/2013, 1:59:32 PM Β· Difficulty 9.8480 Β· 6,680,037 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a8f124d71bfb2bd7a967ab3b594a183f01caa38ccf77cacd52ea2fe1f1a7b349
View on Chainz β†—

Height

#146,541

Difficulty

9.848015

Transactions

1

Size

200 B

Version

2

Bits

09d91783

Nonce

50,333,837

Timestamp

9/2/2013, 1:59:32 PM

Confirmations

6,680,037

Merkle Root

525805bbd15b38c7e36d716c2cdbb0a70b08d006d42d5319b7505aa0da697014
Transactions (1)
Coinbase525805bbd15b38…505aa0da697014
1 in β†’ 1 out10.3000 XPM112 B
AT5A2KL6…CT16n6i2
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.

9.609 Γ— 10⁹⁰(91-digit number)
96094890324568155017…68964781997383616000
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
9.609 Γ— 10⁹⁰(91-digit number)
96094890324568155017…68964781997383615999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.921 Γ— 10⁹¹(92-digit number)
19218978064913631003…37929563994767231999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.843 Γ— 10⁹¹(92-digit number)
38437956129827262006…75859127989534463999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.687 Γ— 10⁹¹(92-digit number)
76875912259654524013…51718255979068927999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.537 Γ— 10⁹²(93-digit number)
15375182451930904802…03436511958137855999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.075 Γ— 10⁹²(93-digit number)
30750364903861809605…06873023916275711999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.150 Γ— 10⁹²(93-digit number)
61500729807723619211…13746047832551423999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.230 Γ— 10⁹³(94-digit number)
12300145961544723842…27492095665102847999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.460 Γ— 10⁹³(94-digit number)
24600291923089447684…54984191330205695999
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 146541

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 a8f124d71bfb2bd7a967ab3b594a183f01caa38ccf77cacd52ea2fe1f1a7b349

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 #146,541 on Chainz β†—
Circulating Supply:57,856,773 XPMΒ·at block #6,826,577 Β· updates every 60s
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