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Home/Chain Registry/Block #3,241,954

Block #3,241,954

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/26/2019, 3:44:00 PM Β· Difficulty 11.0035 Β· 3,601,723 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cd566cfa04be67492df884b2e5924254323d3a0e86424554f4abb46a26bedcca
View on Chainz β†—

Difficulty

11.003531

Transactions

2

Size

573 B

Version

2

Bits

0b00e76d

Nonce

745,956,427

Timestamp

6/26/2019, 3:44:00 PM

Confirmations

3,601,723

Merkle Root

e76323016cdd437e4693e869b00babae5f2cb60edd219554729e1265dc622f05
Transactions (2)
Coinbased32ed614daf76d…3effd69f3231ea
1 in β†’ 1 out8.2600 XPM110 B
ASiq2qtK…VMhmk7yL
e193f03c39dc13…4b8dd8463071c2
2 in β†’ 2 out99.8025 XPM373 B
AeTHTL7A…vT1872bkAHNhNZU4…9kirZbj7
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.

2.081 Γ— 10⁹⁴(95-digit number)
20818736557686189811…49230854936761733120
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
2.081 Γ— 10⁹⁴(95-digit number)
20818736557686189811…49230854936761733119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.081 Γ— 10⁹⁴(95-digit number)
20818736557686189811…49230854936761733121
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
4.163 Γ— 10⁹⁴(95-digit number)
41637473115372379623…98461709873523466239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.163 Γ— 10⁹⁴(95-digit number)
41637473115372379623…98461709873523466241
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
8.327 Γ— 10⁹⁴(95-digit number)
83274946230744759247…96923419747046932479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.327 Γ— 10⁹⁴(95-digit number)
83274946230744759247…96923419747046932481
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
1.665 Γ— 10⁹⁡(96-digit number)
16654989246148951849…93846839494093864959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.665 Γ— 10⁹⁡(96-digit number)
16654989246148951849…93846839494093864961
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
3.330 Γ— 10⁹⁡(96-digit number)
33309978492297903699…87693678988187729919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.330 Γ— 10⁹⁡(96-digit number)
33309978492297903699…87693678988187729921
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
6.661 Γ— 10⁹⁡(96-digit number)
66619956984595807398…75387357976375459839
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 3241954

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 cd566cfa04be67492df884b2e5924254323d3a0e86424554f4abb46a26bedcca

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 #3,241,954 on Chainz β†—
Circulating Supply:57,993,790 XPMΒ·at block #6,843,676 Β· updates every 60s
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