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Block #97,943

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/5/2013, 12:05:46 AM Β· Difficulty 9.3230 Β· 6,714,848 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
26dcb565718a190411f1e546db29ab1f16dc382d813bbffa279a1e7b9c5a025c
View on Chainz β†—

Height

#97,943

Difficulty

9.322970

Transactions

1

Size

200 B

Version

2

Bits

0952ae22

Nonce

98,094

Timestamp

8/5/2013, 12:05:46 AM

Confirmations

6,714,848

Merkle Root

78a515b64e27ed541fe3563dbcbd9e647f05da010298a34e9880ee41ad3271ea
Transactions (1)
Coinbase78a515b64e27ed…80ee41ad3271ea
1 in β†’ 1 out11.4900 XPM109 B
AT3Bb7c7…rCC2CsmN
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.

1.433 Γ— 10⁹⁢(97-digit number)
14332703043903724464…93559055896330342080
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
1.433 Γ— 10⁹⁢(97-digit number)
14332703043903724464…93559055896330342079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.433 Γ— 10⁹⁢(97-digit number)
14332703043903724464…93559055896330342081
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
2.866 Γ— 10⁹⁢(97-digit number)
28665406087807448929…87118111792660684159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.866 Γ— 10⁹⁢(97-digit number)
28665406087807448929…87118111792660684161
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
5.733 Γ— 10⁹⁢(97-digit number)
57330812175614897859…74236223585321368319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.733 Γ— 10⁹⁢(97-digit number)
57330812175614897859…74236223585321368321
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
1.146 Γ— 10⁹⁷(98-digit number)
11466162435122979571…48472447170642736639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.146 Γ— 10⁹⁷(98-digit number)
11466162435122979571…48472447170642736641
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
2.293 Γ— 10⁹⁷(98-digit number)
22932324870245959143…96944894341285473279
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 97943

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 26dcb565718a190411f1e546db29ab1f16dc382d813bbffa279a1e7b9c5a025c

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 #97,943 on Chainz β†—
Circulating Supply:57,746,370 XPMΒ·at block #6,812,790 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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