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Home/Chain Registry/Block #2,142,257

Block #2,142,257

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/2/2017, 7:03:59 PM Β· Difficulty 10.8749 Β· 4,698,231 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b135016ecaadfa0ec8867373457854e5ed6c9b6e118c53846ccd73b1d5c6b5cf
View on Chainz β†—

Difficulty

10.874949

Transactions

1

Size

199 B

Version

2

Bits

0adffcae

Nonce

241,934,856

Timestamp

6/2/2017, 7:03:59 PM

Confirmations

4,698,231

Merkle Root

ec692ae876cc26ac2e553d3ca4a7701ee24117ffb475c40805333b9702df34e1
Transactions (1)
Coinbaseec692ae876cc26…333b9702df34e1
1 in β†’ 1 out8.4400 XPM109 B
AMNpQged…wrvph51f
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.

2.559 Γ— 10⁹⁡(96-digit number)
25590439186380325497…73314860507365161120
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
2.559 Γ— 10⁹⁡(96-digit number)
25590439186380325497…73314860507365161119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.559 Γ— 10⁹⁡(96-digit number)
25590439186380325497…73314860507365161121
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
5.118 Γ— 10⁹⁡(96-digit number)
51180878372760650995…46629721014730322239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.118 Γ— 10⁹⁡(96-digit number)
51180878372760650995…46629721014730322241
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
1.023 Γ— 10⁹⁢(97-digit number)
10236175674552130199…93259442029460644479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.023 Γ— 10⁹⁢(97-digit number)
10236175674552130199…93259442029460644481
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
2.047 Γ— 10⁹⁢(97-digit number)
20472351349104260398…86518884058921288959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.047 Γ— 10⁹⁢(97-digit number)
20472351349104260398…86518884058921288961
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
4.094 Γ— 10⁹⁢(97-digit number)
40944702698208520796…73037768117842577919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.094 Γ— 10⁹⁢(97-digit number)
40944702698208520796…73037768117842577921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2142257

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 b135016ecaadfa0ec8867373457854e5ed6c9b6e118c53846ccd73b1d5c6b5cf

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 #2,142,257 on Chainz β†—
Circulating Supply:57,968,235 XPMΒ·at block #6,840,487 Β· updates every 60s
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