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Block #146,029

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/2/2013, 6:16:06 AM Β· Difficulty 9.8465 Β· 6,654,634 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
528d44b9b2d690c2d3b38a9bd64b09f0b74b94ff464ccc3e23951f47ad98f668
View on Chainz β†—

Height

#146,029

Difficulty

9.846511

Transactions

1

Size

199 B

Version

2

Bits

09d8b4f7

Nonce

191,847

Timestamp

9/2/2013, 6:16:06 AM

Confirmations

6,654,634

Merkle Root

a76c96d146a99d82e8e419688ee0d3beffe7f1bfa01d7d4fcaa4f1ea0e25d42e
Transactions (1)
Coinbasea76c96d146a99d…a4f1ea0e25d42e
1 in β†’ 1 out10.3000 XPM109 B
AHmvhRqW…qgG5FwBR
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.

2.192 Γ— 10⁹⁴(95-digit number)
21922879541045207067…07297827778176573670
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
2.192 Γ— 10⁹⁴(95-digit number)
21922879541045207067…07297827778176573669
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.384 Γ— 10⁹⁴(95-digit number)
43845759082090414134…14595655556353147339
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.769 Γ— 10⁹⁴(95-digit number)
87691518164180828269…29191311112706294679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.753 Γ— 10⁹⁡(96-digit number)
17538303632836165653…58382622225412589359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.507 Γ— 10⁹⁡(96-digit number)
35076607265672331307…16765244450825178719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.015 Γ— 10⁹⁡(96-digit number)
70153214531344662615…33530488901650357439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.403 Γ— 10⁹⁢(97-digit number)
14030642906268932523…67060977803300714879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.806 Γ— 10⁹⁢(97-digit number)
28061285812537865046…34121955606601429759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.612 Γ— 10⁹⁢(97-digit number)
56122571625075730092…68243911213202859519
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 146029

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 528d44b9b2d690c2d3b38a9bd64b09f0b74b94ff464ccc3e23951f47ad98f668

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 #146,029 on Chainz β†—
Circulating Supply:57,649,366 XPMΒ·at block #6,800,662 Β· updates every 60s
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