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Home/Chain Registry/Block #3,095,986

Block #3,095,986

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/16/2019, 4:33:06 PM Β· Difficulty 11.0825 Β· 3,747,879 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
04a7bb3c843a96289bb586625b218945ca22a75f3e5db0bd744a20527b2f5c75
View on Chainz β†—

Difficulty

11.082459

Transactions

1

Size

200 B

Version

2

Bits

0b151c07

Nonce

870,518,055

Timestamp

3/16/2019, 4:33:06 PM

Confirmations

3,747,879

Merkle Root

72cfe0be52d809e6195a843a9b8b1f1ba2995fb98e3749c4fd9f1f213947f2dd
Transactions (1)
Coinbase72cfe0be52d809…9f1f213947f2dd
1 in β†’ 1 out8.1300 XPM110 B
AbXwmGxD…4XXYP765
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.

9.182 Γ— 10⁹³(94-digit number)
91821259456044952261…61422265974931844000
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
9.182 Γ— 10⁹³(94-digit number)
91821259456044952261…61422265974931843999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.182 Γ— 10⁹³(94-digit number)
91821259456044952261…61422265974931844001
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
1.836 Γ— 10⁹⁴(95-digit number)
18364251891208990452…22844531949863687999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.836 Γ— 10⁹⁴(95-digit number)
18364251891208990452…22844531949863688001
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
3.672 Γ— 10⁹⁴(95-digit number)
36728503782417980904…45689063899727375999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.672 Γ— 10⁹⁴(95-digit number)
36728503782417980904…45689063899727376001
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
7.345 Γ— 10⁹⁴(95-digit number)
73457007564835961809…91378127799454751999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.345 Γ— 10⁹⁴(95-digit number)
73457007564835961809…91378127799454752001
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
1.469 Γ— 10⁹⁡(96-digit number)
14691401512967192361…82756255598909503999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.469 Γ— 10⁹⁡(96-digit number)
14691401512967192361…82756255598909504001
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
2.938 Γ— 10⁹⁡(96-digit number)
29382803025934384723…65512511197819007999
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 3095986

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 04a7bb3c843a96289bb586625b218945ca22a75f3e5db0bd744a20527b2f5c75

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 #3,095,986 on Chainz β†—
Circulating Supply:57,995,289 XPMΒ·at block #6,843,864 Β· updates every 60s
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