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Block #80,896

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/24/2013, 10:19:49 AM Β· Difficulty 9.2607 Β· 6,745,183 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4421177cd3bacad1842801e2266535063005a2273773493bed081ab7f75ae01a
View on Chainz β†—

Height

#80,896

Difficulty

9.260674

Transactions

1

Size

203 B

Version

2

Bits

0942bb8c

Nonce

39,375

Timestamp

7/24/2013, 10:19:49 AM

Confirmations

6,745,183

Merkle Root

4b0f362f02349e5299c1ede7db4e7e83be3cbe999e8085a4701d93b369177f79
Transactions (1)
Coinbase4b0f362f02349e…1d93b369177f79
1 in β†’ 1 out11.6400 XPM109 B
AJG5MM5r…9VXaBp6j
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.

3.406 Γ— 10¹⁰³(104-digit number)
34061335235275919841…85950747558711801280
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
3.406 Γ— 10¹⁰³(104-digit number)
34061335235275919841…85950747558711801279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.406 Γ— 10¹⁰³(104-digit number)
34061335235275919841…85950747558711801281
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
6.812 Γ— 10¹⁰³(104-digit number)
68122670470551839683…71901495117423602559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.812 Γ— 10¹⁰³(104-digit number)
68122670470551839683…71901495117423602561
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
1.362 Γ— 10¹⁰⁴(105-digit number)
13624534094110367936…43802990234847205119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.362 Γ— 10¹⁰⁴(105-digit number)
13624534094110367936…43802990234847205121
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
2.724 Γ— 10¹⁰⁴(105-digit number)
27249068188220735873…87605980469694410239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.724 Γ— 10¹⁰⁴(105-digit number)
27249068188220735873…87605980469694410241
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
5.449 Γ— 10¹⁰⁴(105-digit number)
54498136376441471746…75211960939388820479
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 80896

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 4421177cd3bacad1842801e2266535063005a2273773493bed081ab7f75ae01a

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 #80,896 on Chainz β†—
Circulating Supply:57,852,752 XPMΒ·at block #6,826,078 Β· updates every 60s
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