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Home/Chain Registry/Block #3,503,914

Block #3,503,914

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/7/2020, 1:17:05 PM Β· Difficulty 10.9308 Β· 3,335,471 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
39061c7d14a437f14bd6609542ea05792e449cc3dbd7ff9e43a909a57a47cd7c
View on Chainz β†—

Difficulty

10.930846

Transactions

1

Size

201 B

Version

2

Bits

0aee4bf4

Nonce

929,538,874

Timestamp

1/7/2020, 1:17:05 PM

Confirmations

3,335,471

Merkle Root

220e1aae2ddff9bb03bd7d2eb5049c129e95fcabf67a82d3032ae25eb434900c
Transactions (1)
Coinbase220e1aae2ddff9…2ae25eb434900c
1 in β†’ 1 out8.3600 XPM110 B
ASiq2qtK…VMhmk7yL
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.

7.232 Γ— 10⁹⁡(96-digit number)
72321319254304273234…86943712012570324160
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
7.232 Γ— 10⁹⁡(96-digit number)
72321319254304273234…86943712012570324159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.232 Γ— 10⁹⁡(96-digit number)
72321319254304273234…86943712012570324161
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
1.446 Γ— 10⁹⁢(97-digit number)
14464263850860854646…73887424025140648319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.446 Γ— 10⁹⁢(97-digit number)
14464263850860854646…73887424025140648321
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
2.892 Γ— 10⁹⁢(97-digit number)
28928527701721709293…47774848050281296639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.892 Γ— 10⁹⁢(97-digit number)
28928527701721709293…47774848050281296641
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
5.785 Γ— 10⁹⁢(97-digit number)
57857055403443418587…95549696100562593279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.785 Γ— 10⁹⁢(97-digit number)
57857055403443418587…95549696100562593281
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
1.157 Γ— 10⁹⁷(98-digit number)
11571411080688683717…91099392201125186559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.157 Γ— 10⁹⁷(98-digit number)
11571411080688683717…91099392201125186561
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 3503914

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 39061c7d14a437f14bd6609542ea05792e449cc3dbd7ff9e43a909a57a47cd7c

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 #3,503,914 on Chainz β†—
Circulating Supply:57,959,363 XPMΒ·at block #6,839,384 Β· updates every 60s
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