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Block #83,086

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/25/2013, 9:36:46 PM Β· Difficulty 9.2714 Β· 6,729,074 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fa19a9809b99b79f0682b7e8295c1fab478d688ac8e12160e21ab155f2774967
View on Chainz β†—

Height

#83,086

Difficulty

9.271450

Transactions

1

Size

200 B

Version

2

Bits

09457dbb

Nonce

77

Timestamp

7/25/2013, 9:36:46 PM

Confirmations

6,729,074

Merkle Root

d4f4b5a8efdf250550ef1c2471f169c363ef79ee1123df4d197f26705b94707e
Transactions (1)
Coinbased4f4b5a8efdf25…7f26705b94707e
1 in β†’ 1 out11.6200 XPM110 B
AKwPkKuL…AB9QZbHA
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.

1.390 Γ— 10⁹⁡(96-digit number)
13901913773660737956…30548306209771751350
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
1.390 Γ— 10⁹⁡(96-digit number)
13901913773660737956…30548306209771751349
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.390 Γ— 10⁹⁡(96-digit number)
13901913773660737956…30548306209771751351
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
2.780 Γ— 10⁹⁡(96-digit number)
27803827547321475912…61096612419543502699
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.780 Γ— 10⁹⁡(96-digit number)
27803827547321475912…61096612419543502701
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
5.560 Γ— 10⁹⁡(96-digit number)
55607655094642951825…22193224839087005399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.560 Γ— 10⁹⁡(96-digit number)
55607655094642951825…22193224839087005401
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
1.112 Γ— 10⁹⁢(97-digit number)
11121531018928590365…44386449678174010799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.112 Γ— 10⁹⁢(97-digit number)
11121531018928590365…44386449678174010801
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
2.224 Γ— 10⁹⁢(97-digit number)
22243062037857180730…88772899356348021599
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 83086

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 fa19a9809b99b79f0682b7e8295c1fab478d688ac8e12160e21ab155f2774967

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 #83,086 on Chainz β†—
Circulating Supply:57,741,298 XPMΒ·at block #6,812,159 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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