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Home/Chain Registry/Block #1,681,449

Block #1,681,449

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2016, 8:49:03 AM Β· Difficulty 10.7154 Β· 5,160,872 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6ea92214ef7710aef8ac7a4468a41ca79f8c35fafc3908cb464ab22cd330714a
View on Chainz β†—

Difficulty

10.715372

Transactions

1

Size

243 B

Version

2

Bits

0ab7229d

Nonce

505,395,345

Timestamp

7/20/2016, 8:49:03 AM

Confirmations

5,160,872

Merkle Root

0ff2cdc370c7b344ff365123fe4a6689deae999c200e32eeea3c72145ced9289
Transactions (1)
Coinbase0ff2cdc370c7b3…3c72145ced9289
1 in β†’ 2 out8.7000 XPM152 B
AVsg8K1F…ZPDrnoURALPu3s2c…EJXLjVFh
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.

2.971 Γ— 10⁹⁷(98-digit number)
29712626274918453811…21495978279720043520
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
2.971 Γ— 10⁹⁷(98-digit number)
29712626274918453811…21495978279720043519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.942 Γ— 10⁹⁷(98-digit number)
59425252549836907623…42991956559440087039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.188 Γ— 10⁹⁸(99-digit number)
11885050509967381524…85983913118880174079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.377 Γ— 10⁹⁸(99-digit number)
23770101019934763049…71967826237760348159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.754 Γ— 10⁹⁸(99-digit number)
47540202039869526099…43935652475520696319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.508 Γ— 10⁹⁸(99-digit number)
95080404079739052198…87871304951041392639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.901 Γ— 10⁹⁹(100-digit number)
19016080815947810439…75742609902082785279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.803 Γ— 10⁹⁹(100-digit number)
38032161631895620879…51485219804165570559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.606 Γ— 10⁹⁹(100-digit number)
76064323263791241758…02970439608331141119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.521 Γ— 10¹⁰⁰(101-digit number)
15212864652758248351…05940879216662282239
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 1681449

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 6ea92214ef7710aef8ac7a4468a41ca79f8c35fafc3908cb464ab22cd330714a

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 #1,681,449 on Chainz β†—
Circulating Supply:57,982,974 XPMΒ·at block #6,842,320 Β· updates every 60s
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