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Block #144,027

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/1/2013, 1:41:34 AM Β· Difficulty 9.8374 Β· 6,652,481 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3a1b29a2d7c93ec47c603570d7be27397e6c775d06b941411dd851e729f9a5bb
View on Chainz β†—

Height

#144,027

Difficulty

9.837396

Transactions

1

Size

200 B

Version

2

Bits

09d65f9c

Nonce

7,899

Timestamp

9/1/2013, 1:41:34 AM

Confirmations

6,652,481

Merkle Root

e02364df6c0c3a9f2953a8d5623cb7adfca8437edef7156e2134aa7eb05a31de
Transactions (1)
Coinbasee02364df6c0c3a…34aa7eb05a31de
1 in β†’ 1 out10.3200 XPM109 B
AMToov5r…VbPfT6j8
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.

1.027 Γ— 10⁹⁢(97-digit number)
10279906826341650695…42681213233961761600
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
1.027 Γ— 10⁹⁢(97-digit number)
10279906826341650695…42681213233961761599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.055 Γ— 10⁹⁢(97-digit number)
20559813652683301390…85362426467923523199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.111 Γ— 10⁹⁢(97-digit number)
41119627305366602781…70724852935847046399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.223 Γ— 10⁹⁢(97-digit number)
82239254610733205563…41449705871694092799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.644 Γ— 10⁹⁷(98-digit number)
16447850922146641112…82899411743388185599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.289 Γ— 10⁹⁷(98-digit number)
32895701844293282225…65798823486776371199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.579 Γ— 10⁹⁷(98-digit number)
65791403688586564451…31597646973552742399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.315 Γ— 10⁹⁸(99-digit number)
13158280737717312890…63195293947105484799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.631 Γ— 10⁹⁸(99-digit number)
26316561475434625780…26390587894210969599
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 144027

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 3a1b29a2d7c93ec47c603570d7be27397e6c775d06b941411dd851e729f9a5bb

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 #144,027 on Chainz β†—
Circulating Supply:57,616,066 XPMΒ·at block #6,796,507 Β· updates every 60s
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