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Home/Chain Registry/Block #3,142,131

Block #3,142,131

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/16/2019, 5:07:36 PM Β· Difficulty 11.3163 Β· 3,691,087 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
57430cddc064606950173b0b8e5b4adfdb19938f813064c32b383dca49e1146a
View on Chainz β†—

Difficulty

11.316290

Transactions

1

Size

200 B

Version

2

Bits

0b50f86a

Nonce

295,684,022

Timestamp

4/16/2019, 5:07:36 PM

Confirmations

3,691,087

Merkle Root

1b42a579f41c4f66d0c63d08d30fdf18ce4c98e30bd938fb885b46eff3e065e6
Transactions (1)
Coinbase1b42a579f41c4f…5b46eff3e065e6
1 in β†’ 1 out7.8000 XPM110 B
ARbm48qR…9xQc8DBX
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.

8.186 Γ— 10⁹⁴(95-digit number)
81863091405184693906…94766888541068791840
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
8.186 Γ— 10⁹⁴(95-digit number)
81863091405184693906…94766888541068791839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.186 Γ— 10⁹⁴(95-digit number)
81863091405184693906…94766888541068791841
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
1.637 Γ— 10⁹⁡(96-digit number)
16372618281036938781…89533777082137583679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.637 Γ— 10⁹⁡(96-digit number)
16372618281036938781…89533777082137583681
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
3.274 Γ— 10⁹⁡(96-digit number)
32745236562073877562…79067554164275167359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.274 Γ— 10⁹⁡(96-digit number)
32745236562073877562…79067554164275167361
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
6.549 Γ— 10⁹⁡(96-digit number)
65490473124147755125…58135108328550334719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.549 Γ— 10⁹⁡(96-digit number)
65490473124147755125…58135108328550334721
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
1.309 Γ— 10⁹⁢(97-digit number)
13098094624829551025…16270216657100669439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.309 Γ— 10⁹⁢(97-digit number)
13098094624829551025…16270216657100669441
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
2.619 Γ— 10⁹⁢(97-digit number)
26196189249659102050…32540433314201338879
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 3142131

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 57430cddc064606950173b0b8e5b4adfdb19938f813064c32b383dca49e1146a

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 #3,142,131 on Chainz β†—
Circulating Supply:57,909,931 XPMΒ·at block #6,833,217 Β· updates every 60s
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