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Home/Chain Registry/Block #2,910,142

Block #2,910,142

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/4/2018, 6:21:04 PM Β· Difficulty 11.5355 Β· 3,930,297 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
920ca35e96bc12f772d76d2c48e6b52f7f7833ac1f0cc7e3e81cf030b71863af
View on Chainz β†—

Difficulty

11.535488

Transactions

1

Size

200 B

Version

2

Bits

0b8915bc

Nonce

337,030,824

Timestamp

11/4/2018, 6:21:04 PM

Confirmations

3,930,297

Merkle Root

fd0ede3dd5edb205675614b03192ec47907b4583f756012159ecbed0ca7cdb17
Transactions (1)
Coinbasefd0ede3dd5edb2…ecbed0ca7cdb17
1 in β†’ 1 out7.5000 XPM110 B
ASBvBLqg…SyghyjwF
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.

2.578 Γ— 10⁹⁴(95-digit number)
25786830924949343274…59450037648761373160
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
2.578 Γ— 10⁹⁴(95-digit number)
25786830924949343274…59450037648761373159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.578 Γ— 10⁹⁴(95-digit number)
25786830924949343274…59450037648761373161
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
5.157 Γ— 10⁹⁴(95-digit number)
51573661849898686548…18900075297522746319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.157 Γ— 10⁹⁴(95-digit number)
51573661849898686548…18900075297522746321
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
1.031 Γ— 10⁹⁡(96-digit number)
10314732369979737309…37800150595045492639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.031 Γ— 10⁹⁡(96-digit number)
10314732369979737309…37800150595045492641
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
2.062 Γ— 10⁹⁡(96-digit number)
20629464739959474619…75600301190090985279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.062 Γ— 10⁹⁡(96-digit number)
20629464739959474619…75600301190090985281
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
4.125 Γ— 10⁹⁡(96-digit number)
41258929479918949238…51200602380181970559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.125 Γ— 10⁹⁡(96-digit number)
41258929479918949238…51200602380181970561
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
8.251 Γ— 10⁹⁡(96-digit number)
82517858959837898477…02401204760363941119
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 2910142

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 920ca35e96bc12f772d76d2c48e6b52f7f7833ac1f0cc7e3e81cf030b71863af

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 #2,910,142 on Chainz β†—
Circulating Supply:57,967,840 XPMΒ·at block #6,840,438 Β· updates every 60s
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