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Home/Chain Registry/Block #1,589,192

Block #1,589,192

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/17/2016, 11:08:03 PM Β· Difficulty 10.6520 Β· 5,249,087 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
302a8d14926dbdd5edc5b8089f5de22a1568e4c8a2c8a6335ea670e2813ff11d
View on Chainz β†—

Difficulty

10.652023

Transactions

1

Size

198 B

Version

2

Bits

0aa6eb02

Nonce

1,438,923,221

Timestamp

5/17/2016, 11:08:03 PM

Confirmations

5,249,087

Merkle Root

1c9633c009f998a2686a29413746acac66cc05db35b6fe01a7092feaf3bbd2e8
Transactions (1)
Coinbase1c9633c009f998…092feaf3bbd2e8
1 in β†’ 1 out8.8000 XPM109 B
Ab5VrDQ4…SPiLLRhK
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.

2.169 Γ— 10⁹²(93-digit number)
21696462959596512861…03926942673865737600
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
2.169 Γ— 10⁹²(93-digit number)
21696462959596512861…03926942673865737599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.339 Γ— 10⁹²(93-digit number)
43392925919193025723…07853885347731475199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.678 Γ— 10⁹²(93-digit number)
86785851838386051447…15707770695462950399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.735 Γ— 10⁹³(94-digit number)
17357170367677210289…31415541390925900799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.471 Γ— 10⁹³(94-digit number)
34714340735354420579…62831082781851801599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.942 Γ— 10⁹³(94-digit number)
69428681470708841158…25662165563703603199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.388 Γ— 10⁹⁴(95-digit number)
13885736294141768231…51324331127407206399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.777 Γ— 10⁹⁴(95-digit number)
27771472588283536463…02648662254814412799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.554 Γ— 10⁹⁴(95-digit number)
55542945176567072926…05297324509628825599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.110 Γ— 10⁹⁡(96-digit number)
11108589035313414585…10594649019257651199
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 1589192

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 302a8d14926dbdd5edc5b8089f5de22a1568e4c8a2c8a6335ea670e2813ff11d

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 #1,589,192 on Chainz β†—
Circulating Supply:57,950,513 XPMΒ·at block #6,838,278 Β· updates every 60s
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