XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #3,051,935

Block #3,051,935

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/14/2019, 2:18:44 AM Β· Difficulty 11.0005 Β· 3,787,864 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7dbfe598bdce39e1a7729e02a6d799bfba39b61ed19581aa18c2b980a4ec2b1c
View on Chainz β†—

Difficulty

11.000484

Transactions

1

Size

201 B

Version

2

Bits

0b001fb4

Nonce

406,880,442

Timestamp

2/14/2019, 2:18:44 AM

Confirmations

3,787,864

Merkle Root

f624c320ac15cee6eca31acb31f0c0f5412a46d8b98fa7415d85c08f3bb6f70a
Transactions (1)
Coinbasef624c320ac15ce…85c08f3bb6f70a
1 in β†’ 1 out8.2500 XPM110 B
AbXwmGxD…4XXYP765
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.

2.382 Γ— 10⁹⁢(97-digit number)
23820566599941909813…53726027887248670720
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
2.382 Γ— 10⁹⁢(97-digit number)
23820566599941909813…53726027887248670719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.382 Γ— 10⁹⁢(97-digit number)
23820566599941909813…53726027887248670721
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
4.764 Γ— 10⁹⁢(97-digit number)
47641133199883819627…07452055774497341439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.764 Γ— 10⁹⁢(97-digit number)
47641133199883819627…07452055774497341441
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
9.528 Γ— 10⁹⁢(97-digit number)
95282266399767639254…14904111548994682879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.528 Γ— 10⁹⁢(97-digit number)
95282266399767639254…14904111548994682881
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
1.905 Γ— 10⁹⁷(98-digit number)
19056453279953527850…29808223097989365759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.905 Γ— 10⁹⁷(98-digit number)
19056453279953527850…29808223097989365761
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
3.811 Γ— 10⁹⁷(98-digit number)
38112906559907055701…59616446195978731519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.811 Γ— 10⁹⁷(98-digit number)
38112906559907055701…59616446195978731521
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
7.622 Γ— 10⁹⁷(98-digit number)
76225813119814111403…19232892391957463039
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 3051935

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 7dbfe598bdce39e1a7729e02a6d799bfba39b61ed19581aa18c2b980a4ec2b1c

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 #3,051,935 on Chainz β†—
Circulating Supply:57,962,684 XPMΒ·at block #6,839,798 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy