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Block #311,751

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/14/2013, 5:12:52 PM Β· Difficulty 9.9956 Β· 6,489,088 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f9565fe02e3ded76d63b6cf7c7b8e22c197153e45fe783b83b9539c632dc0bfa
View on Chainz β†—

Height

#311,751

Difficulty

9.995591

Transactions

1

Size

208 B

Version

2

Bits

09fedf0f

Nonce

196,500

Timestamp

12/14/2013, 5:12:52 PM

Confirmations

6,489,088

Merkle Root

24e1e2e5899f0dccb0e60f37acd592ec0f660724e88329cda17f807e01188462
Transactions (1)
Coinbase24e1e2e5899f0d…7f807e01188462
1 in β†’ 1 out9.9900 XPM116 B
AbwWkWZt…kawDhufa
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.

3.753 Γ— 10⁹⁸(99-digit number)
37538043783947258865…46334724412234566080
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
3.753 Γ— 10⁹⁸(99-digit number)
37538043783947258865…46334724412234566079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.753 Γ— 10⁹⁸(99-digit number)
37538043783947258865…46334724412234566081
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
7.507 Γ— 10⁹⁸(99-digit number)
75076087567894517730…92669448824469132159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.507 Γ— 10⁹⁸(99-digit number)
75076087567894517730…92669448824469132161
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
1.501 Γ— 10⁹⁹(100-digit number)
15015217513578903546…85338897648938264319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.501 Γ— 10⁹⁹(100-digit number)
15015217513578903546…85338897648938264321
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
3.003 Γ— 10⁹⁹(100-digit number)
30030435027157807092…70677795297876528639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.003 Γ— 10⁹⁹(100-digit number)
30030435027157807092…70677795297876528641
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
6.006 Γ— 10⁹⁹(100-digit number)
60060870054315614184…41355590595753057279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.006 Γ— 10⁹⁹(100-digit number)
60060870054315614184…41355590595753057281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 311751

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 f9565fe02e3ded76d63b6cf7c7b8e22c197153e45fe783b83b9539c632dc0bfa

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 #311,751 on Chainz β†—
Circulating Supply:57,650,770 XPMΒ·at block #6,800,838 Β· updates every 60s
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