XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #102,599

Block #102,599

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/7/2013, 5:01:54 AM Β· Difficulty 9.4993 Β· 6,714,236 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
fb4ab5f6563ed7269d987566fc2518573f4d980d6e03a05cf4526ca50fb10db7
View on Chainz β†—

Height

#102,599

Difficulty

9.499308

Transactions

2

Size

397 B

Version

2

Bits

097fd2a4

Nonce

12,589

Timestamp

8/7/2013, 5:01:54 AM

Confirmations

6,714,236

Merkle Root

97ae03077ad33f8aac25a1393c198e313c9065c472b7818e9acc3ae2d8e0e18e
Transactions (2)
Coinbaseff36e763834a14…835b9bbb100856
1 in β†’ 1 out11.0800 XPM109 B
AWd92XeW…9AH43S2X
e0e5eea99930f5…339ea7c0dbcad6
1 in β†’ 1 out5.6650 XPM193 B
AeguK5Ai…CLUqoF9q
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.

2.868 Γ— 10¹⁰⁡(106-digit number)
28680714020965660099…47299162451216603360
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
2.868 Γ— 10¹⁰⁡(106-digit number)
28680714020965660099…47299162451216603359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.868 Γ— 10¹⁰⁡(106-digit number)
28680714020965660099…47299162451216603361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
5.736 Γ— 10¹⁰⁡(106-digit number)
57361428041931320198…94598324902433206719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.736 Γ— 10¹⁰⁡(106-digit number)
57361428041931320198…94598324902433206721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
1.147 Γ— 10¹⁰⁢(107-digit number)
11472285608386264039…89196649804866413439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.147 Γ— 10¹⁰⁢(107-digit number)
11472285608386264039…89196649804866413441
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
2.294 Γ— 10¹⁰⁢(107-digit number)
22944571216772528079…78393299609732826879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.294 Γ— 10¹⁰⁢(107-digit number)
22944571216772528079…78393299609732826881
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
4.588 Γ— 10¹⁰⁢(107-digit number)
45889142433545056158…56786599219465653759
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 Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 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 102599

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 fb4ab5f6563ed7269d987566fc2518573f4d980d6e03a05cf4526ca50fb10db7

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 #102,599 on Chainz β†—
Circulating Supply:57,778,720 XPMΒ·at block #6,816,834 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy