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Home/Chain Registry/Block #2,934,522

Block #2,934,522

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/22/2018, 3:19:06 PM Β· Difficulty 11.3931 Β· 3,903,852 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
514a8f315b8cbb251551e3a2b29c2fb6b98e829f2eba0bdfb42d8d0e3d4a0b42
View on Chainz β†—

Difficulty

11.393063

Transactions

1

Size

201 B

Version

2

Bits

0b649fbf

Nonce

1,209,533,272

Timestamp

11/22/2018, 3:19:06 PM

Confirmations

3,903,852

Merkle Root

0dab884218b7786fdce81d4e4edab4cc02d8b40e3b52ee83b003fd52317f7ff1
Transactions (1)
Coinbase0dab884218b778…03fd52317f7ff1
1 in β†’ 1 out7.6900 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.

3.098 Γ— 10⁹⁷(98-digit number)
30987552508796382802…48174710431571312640
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
3.098 Γ— 10⁹⁷(98-digit number)
30987552508796382802…48174710431571312639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.098 Γ— 10⁹⁷(98-digit number)
30987552508796382802…48174710431571312641
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
6.197 Γ— 10⁹⁷(98-digit number)
61975105017592765605…96349420863142625279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.197 Γ— 10⁹⁷(98-digit number)
61975105017592765605…96349420863142625281
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
1.239 Γ— 10⁹⁸(99-digit number)
12395021003518553121…92698841726285250559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.239 Γ— 10⁹⁸(99-digit number)
12395021003518553121…92698841726285250561
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
2.479 Γ— 10⁹⁸(99-digit number)
24790042007037106242…85397683452570501119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.479 Γ— 10⁹⁸(99-digit number)
24790042007037106242…85397683452570501121
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
4.958 Γ— 10⁹⁸(99-digit number)
49580084014074212484…70795366905141002239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.958 Γ— 10⁹⁸(99-digit number)
49580084014074212484…70795366905141002241
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
9.916 Γ— 10⁹⁸(99-digit number)
99160168028148424969…41590733810282004479
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 2934522

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 514a8f315b8cbb251551e3a2b29c2fb6b98e829f2eba0bdfb42d8d0e3d4a0b42

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 #2,934,522 on Chainz β†—
Circulating Supply:57,951,262 XPMΒ·at block #6,838,373 Β· updates every 60s
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