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Block #143,448

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/31/2013, 4:03:10 PM Β· Difficulty 9.8374 Β· 6,693,575 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0bdbc38e8d47cbf821c39b42495ae60c36f7d44e4b8c46c6eb1b79e22072bd15
View on Chainz β†—

Height

#143,448

Difficulty

9.837374

Transactions

1

Size

199 B

Version

2

Bits

09d65e29

Nonce

23,751

Timestamp

8/31/2013, 4:03:10 PM

Confirmations

6,693,575

Merkle Root

97729711aabc9b8051ff9949679141cc3101dae12877eb5590f70b8cef13dd55
Transactions (1)
Coinbase97729711aabc9b…f70b8cef13dd55
1 in β†’ 1 out10.3200 XPM109 B
AVv2Uokw…Djqkjjws
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.

3.661 Γ— 10⁹³(94-digit number)
36615946959742143370…42539608966846991680
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
3.661 Γ— 10⁹³(94-digit number)
36615946959742143370…42539608966846991679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.323 Γ— 10⁹³(94-digit number)
73231893919484286741…85079217933693983359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.464 Γ— 10⁹⁴(95-digit number)
14646378783896857348…70158435867387966719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.929 Γ— 10⁹⁴(95-digit number)
29292757567793714696…40316871734775933439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.858 Γ— 10⁹⁴(95-digit number)
58585515135587429392…80633743469551866879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.171 Γ— 10⁹⁡(96-digit number)
11717103027117485878…61267486939103733759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.343 Γ— 10⁹⁡(96-digit number)
23434206054234971757…22534973878207467519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.686 Γ— 10⁹⁡(96-digit number)
46868412108469943514…45069947756414935039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.373 Γ— 10⁹⁡(96-digit number)
93736824216939887028…90139895512829870079
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 143448

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 0bdbc38e8d47cbf821c39b42495ae60c36f7d44e4b8c46c6eb1b79e22072bd15

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 #143,448 on Chainz β†—
Circulating Supply:57,940,482 XPMΒ·at block #6,837,022 Β· updates every 60s
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