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Block #296,149

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/5/2013, 8:21:55 PM Β· Difficulty 9.9916 Β· 6,516,737 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2d8a56a5bf13d1ea4abe9c28bb7d02d85d3cbeba73d8c2e548fe4ddecd708dc5
View on Chainz β†—

Height

#296,149

Difficulty

9.991640

Transactions

1

Size

208 B

Version

2

Bits

09fddc18

Nonce

10,568

Timestamp

12/5/2013, 8:21:55 PM

Confirmations

6,516,737

Merkle Root

19cfa0dc2493b80af736805b5c632f7b0ae2347ac6aaf585323fa954d0765c3c
Transactions (1)
Coinbase19cfa0dc2493b8…3fa954d0765c3c
1 in β†’ 1 out10.0000 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.100 Γ— 10¹⁰⁰(101-digit number)
11005250686233153348…35348792800658309120
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
1.100 Γ— 10¹⁰⁰(101-digit number)
11005250686233153348…35348792800658309119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.201 Γ— 10¹⁰⁰(101-digit number)
22010501372466306696…70697585601316618239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.402 Γ— 10¹⁰⁰(101-digit number)
44021002744932613393…41395171202633236479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.804 Γ— 10¹⁰⁰(101-digit number)
88042005489865226786…82790342405266472959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.760 Γ— 10¹⁰¹(102-digit number)
17608401097973045357…65580684810532945919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.521 Γ— 10¹⁰¹(102-digit number)
35216802195946090714…31161369621065891839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.043 Γ— 10¹⁰¹(102-digit number)
70433604391892181429…62322739242131783679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.408 Γ— 10¹⁰²(103-digit number)
14086720878378436285…24645478484263567359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.817 Γ— 10¹⁰²(103-digit number)
28173441756756872571…49290956968527134719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.634 Γ— 10¹⁰²(103-digit number)
56346883513513745143…98581913937054269439
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 296149

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 2d8a56a5bf13d1ea4abe9c28bb7d02d85d3cbeba73d8c2e548fe4ddecd708dc5

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 #296,149 on Chainz β†—
Circulating Supply:57,747,118 XPMΒ·at block #6,812,885 Β· updates every 60s
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