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Home/Chain Registry/Block #2,879,413

Block #2,879,413

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/13/2018, 12:56:26 PM Β· Difficulty 11.6383 Β· 3,962,926 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
03b8ef8dad4ca564bd3914fb6d3d0af750c100da7df89a064b8b8a98ae9fdc06
View on Chainz β†—

Difficulty

11.638339

Transactions

1

Size

200 B

Version

2

Bits

0ba36a34

Nonce

1,752,552,783

Timestamp

10/13/2018, 12:56:26 PM

Confirmations

3,962,926

Merkle Root

29dba88b14076caebb2cedfaa8e0b8619fc7b3ad67856dc35fa2159306b93aa8
Transactions (1)
Coinbase29dba88b14076c…a2159306b93aa8
1 in β†’ 1 out7.3700 XPM110 B
AWquFEHH…A6LP92is
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.

1.336 Γ— 10⁹⁴(95-digit number)
13366159323685398034…88526032470412226120
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
1.336 Γ— 10⁹⁴(95-digit number)
13366159323685398034…88526032470412226119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.336 Γ— 10⁹⁴(95-digit number)
13366159323685398034…88526032470412226121
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
2.673 Γ— 10⁹⁴(95-digit number)
26732318647370796068…77052064940824452239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.673 Γ— 10⁹⁴(95-digit number)
26732318647370796068…77052064940824452241
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
5.346 Γ— 10⁹⁴(95-digit number)
53464637294741592136…54104129881648904479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.346 Γ— 10⁹⁴(95-digit number)
53464637294741592136…54104129881648904481
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
1.069 Γ— 10⁹⁡(96-digit number)
10692927458948318427…08208259763297808959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.069 Γ— 10⁹⁡(96-digit number)
10692927458948318427…08208259763297808961
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
2.138 Γ— 10⁹⁡(96-digit number)
21385854917896636854…16416519526595617919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.138 Γ— 10⁹⁡(96-digit number)
21385854917896636854…16416519526595617921
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
4.277 Γ— 10⁹⁡(96-digit number)
42771709835793273709…32833039053191235839
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 2879413

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 03b8ef8dad4ca564bd3914fb6d3d0af750c100da7df89a064b8b8a98ae9fdc06

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 #2,879,413 on Chainz β†—
Circulating Supply:57,983,119 XPMΒ·at block #6,842,338 Β· updates every 60s
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