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Home/Chain Registry/Block #3,096,839

Block #3,096,839

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/17/2019, 6:12:42 AM Β· Difficulty 11.0885 Β· 3,748,778 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b9b966f4bfa336d091ee92f162a66646086b90de59740a984d9fab29572f5659
View on Chainz β†—

Difficulty

11.088529

Transactions

1

Size

200 B

Version

2

Bits

0b16a9d6

Nonce

1,888,638,017

Timestamp

3/17/2019, 6:12:42 AM

Confirmations

3,748,778

Merkle Root

290b6b4ae7e58cb9c4930592546a96e965d035187bc2e20ba3b1d2235a562320
Transactions (1)
Coinbase290b6b4ae7e58c…b1d2235a562320
1 in β†’ 1 out8.1200 XPM110 B
AUMQRepm…tAfKmdW1
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.

3.784 Γ— 10⁹⁴(95-digit number)
37849733375146832529…59829767091626307600
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
3.784 Γ— 10⁹⁴(95-digit number)
37849733375146832529…59829767091626307599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.784 Γ— 10⁹⁴(95-digit number)
37849733375146832529…59829767091626307601
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
7.569 Γ— 10⁹⁴(95-digit number)
75699466750293665059…19659534183252615199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.569 Γ— 10⁹⁴(95-digit number)
75699466750293665059…19659534183252615201
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
1.513 Γ— 10⁹⁡(96-digit number)
15139893350058733011…39319068366505230399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.513 Γ— 10⁹⁡(96-digit number)
15139893350058733011…39319068366505230401
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
3.027 Γ— 10⁹⁡(96-digit number)
30279786700117466023…78638136733010460799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.027 Γ— 10⁹⁡(96-digit number)
30279786700117466023…78638136733010460801
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
6.055 Γ— 10⁹⁡(96-digit number)
60559573400234932047…57276273466020921599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.055 Γ— 10⁹⁡(96-digit number)
60559573400234932047…57276273466020921601
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
1.211 Γ— 10⁹⁢(97-digit number)
12111914680046986409…14552546932041843199
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 3096839

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 b9b966f4bfa336d091ee92f162a66646086b90de59740a984d9fab29572f5659

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 #3,096,839 on Chainz β†—
Circulating Supply:58,009,383 XPMΒ·at block #6,845,616 Β· updates every 60s
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