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Home/Chain Registry/Block #2,994,928

Block #2,994,928

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/4/2019, 5:54:22 AM Β· Difficulty 11.2699 Β· 3,836,521 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e2334d97bb4dbe58980cd199439ba73e9faa9f77bdfa009222e15cf480a3e85c
View on Chainz β†—

Difficulty

11.269856

Transactions

1

Size

200 B

Version

2

Bits

0b451543

Nonce

1,492,539,581

Timestamp

1/4/2019, 5:54:22 AM

Confirmations

3,836,521

Merkle Root

de3fe2df89347506d444f442a91b0372276c4633ffd21b151d240e1e3742d07d
Transactions (1)
Coinbasede3fe2df893475…240e1e3742d07d
1 in β†’ 1 out7.8600 XPM110 B
AUhjokok…k5m93PZR
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.

2.477 Γ— 10⁹³(94-digit number)
24773120444825846246…70323142207665012340
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
2.477 Γ— 10⁹³(94-digit number)
24773120444825846246…70323142207665012339
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.477 Γ— 10⁹³(94-digit number)
24773120444825846246…70323142207665012341
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
4.954 Γ— 10⁹³(94-digit number)
49546240889651692492…40646284415330024679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.954 Γ— 10⁹³(94-digit number)
49546240889651692492…40646284415330024681
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
9.909 Γ— 10⁹³(94-digit number)
99092481779303384985…81292568830660049359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.909 Γ— 10⁹³(94-digit number)
99092481779303384985…81292568830660049361
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
1.981 Γ— 10⁹⁴(95-digit number)
19818496355860676997…62585137661320098719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.981 Γ— 10⁹⁴(95-digit number)
19818496355860676997…62585137661320098721
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
3.963 Γ— 10⁹⁴(95-digit number)
39636992711721353994…25170275322640197439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.963 Γ— 10⁹⁴(95-digit number)
39636992711721353994…25170275322640197441
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
7.927 Γ— 10⁹⁴(95-digit number)
79273985423442707988…50340550645280394879
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 2994928

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 e2334d97bb4dbe58980cd199439ba73e9faa9f77bdfa009222e15cf480a3e85c

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 #2,994,928 on Chainz β†—
Circulating Supply:57,895,757 XPMΒ·at block #6,831,448 Β· updates every 60s
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