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Block #89,197

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/30/2013, 4:45:49 AM Β· Difficulty 9.2605 Β· 6,705,328 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
edba92e0cb2031553a9242df95646e0d3bf065d46b911c9dbb58a7b668a4156b
View on Chainz β†—

Height

#89,197

Difficulty

9.260478

Transactions

1

Size

204 B

Version

2

Bits

0942aeb3

Nonce

38,567

Timestamp

7/30/2013, 4:45:49 AM

Confirmations

6,705,328

Merkle Root

1250c5cce9f7d89880c22ee998fdcdf7a40f2986ef02a3a7b92772a70fc872f6
Transactions (1)
Coinbase1250c5cce9f7d8…2772a70fc872f6
1 in β†’ 1 out11.6400 XPM109 B
Ad6pA3xv…CgV7gpF4
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.

1.553 Γ— 10¹⁰⁷(108-digit number)
15538216668163004417…57096968509217178210
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
1.553 Γ— 10¹⁰⁷(108-digit number)
15538216668163004417…57096968509217178209
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.553 Γ— 10¹⁰⁷(108-digit number)
15538216668163004417…57096968509217178211
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
3.107 Γ— 10¹⁰⁷(108-digit number)
31076433336326008835…14193937018434356419
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.107 Γ— 10¹⁰⁷(108-digit number)
31076433336326008835…14193937018434356421
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
6.215 Γ— 10¹⁰⁷(108-digit number)
62152866672652017671…28387874036868712839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.215 Γ— 10¹⁰⁷(108-digit number)
62152866672652017671…28387874036868712841
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
1.243 Γ— 10¹⁰⁸(109-digit number)
12430573334530403534…56775748073737425679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.243 Γ— 10¹⁰⁸(109-digit number)
12430573334530403534…56775748073737425681
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
2.486 Γ— 10¹⁰⁸(109-digit number)
24861146669060807068…13551496147474851359
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 89197

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 edba92e0cb2031553a9242df95646e0d3bf065d46b911c9dbb58a7b668a4156b

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 #89,197 on Chainz β†—
Circulating Supply:57,600,239 XPMΒ·at block #6,794,524 Β· updates every 60s
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