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Home/Chain Registry/Block #2,716,249

Block #2,716,249

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/22/2018, 9:31:40 AM Β· Difficulty 11.6142 Β· 4,124,116 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4ee4a9dea8c42f2278ebe388fbf417e3f10f3f399ecdf072e873e844edd3f980
View on Chainz β†—

Difficulty

11.614193

Transactions

1

Size

200 B

Version

2

Bits

0b9d3bbc

Nonce

350,879,767

Timestamp

6/22/2018, 9:31:40 AM

Confirmations

4,124,116

Merkle Root

6f985836a71a2c6455242c9e0f3e29104162fe20738b313404561eb49534c0e5
Transactions (1)
Coinbase6f985836a71a2c…561eb49534c0e5
1 in β†’ 1 out7.4000 XPM110 B
Abxaeiuf…hEU4WmkL
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.

3.703 Γ— 10⁹³(94-digit number)
37038982934731522995…02634234992123891700
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
3.703 Γ— 10⁹³(94-digit number)
37038982934731522995…02634234992123891699
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.703 Γ— 10⁹³(94-digit number)
37038982934731522995…02634234992123891701
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
7.407 Γ— 10⁹³(94-digit number)
74077965869463045991…05268469984247783399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.407 Γ— 10⁹³(94-digit number)
74077965869463045991…05268469984247783401
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
1.481 Γ— 10⁹⁴(95-digit number)
14815593173892609198…10536939968495566799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.481 Γ— 10⁹⁴(95-digit number)
14815593173892609198…10536939968495566801
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
2.963 Γ— 10⁹⁴(95-digit number)
29631186347785218396…21073879936991133599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.963 Γ— 10⁹⁴(95-digit number)
29631186347785218396…21073879936991133601
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
5.926 Γ— 10⁹⁴(95-digit number)
59262372695570436793…42147759873982267199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.926 Γ— 10⁹⁴(95-digit number)
59262372695570436793…42147759873982267201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.185 Γ— 10⁹⁡(96-digit number)
11852474539114087358…84295519747964534399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2716249

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 4ee4a9dea8c42f2278ebe388fbf417e3f10f3f399ecdf072e873e844edd3f980

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 #2,716,249 on Chainz β†—
Circulating Supply:57,967,238 XPMΒ·at block #6,840,364 Β· updates every 60s
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