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Home/Chain Registry/Block #3,850,453

Block #3,850,453

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/8/2020, 12:03:09 PM Β· Difficulty 10.7869 Β· 2,990,881 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6c1d5b0344086d9e264ffc4334d8ec98c245902f939d76297ab4ea598e9a4eaa
View on Chainz β†—

Difficulty

10.786921

Transactions

1

Size

201 B

Version

2

Bits

0ac973aa

Nonce

983,602,151

Timestamp

9/8/2020, 12:03:09 PM

Confirmations

2,990,881

Merkle Root

b884ce8f0520a1f728bf2b8703db8f06d039e55eef8cbfadacefcb43c0160c6e
Transactions (1)
Coinbaseb884ce8f0520a1…efcb43c0160c6e
1 in β†’ 1 out8.5800 XPM109 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.

4.431 Γ— 10⁹⁸(99-digit number)
44319289342451611129…25512237535297290240
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
4.431 Γ— 10⁹⁸(99-digit number)
44319289342451611129…25512237535297290239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.431 Γ— 10⁹⁸(99-digit number)
44319289342451611129…25512237535297290241
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
8.863 Γ— 10⁹⁸(99-digit number)
88638578684903222258…51024475070594580479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.863 Γ— 10⁹⁸(99-digit number)
88638578684903222258…51024475070594580481
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
1.772 Γ— 10⁹⁹(100-digit number)
17727715736980644451…02048950141189160959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.772 Γ— 10⁹⁹(100-digit number)
17727715736980644451…02048950141189160961
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
3.545 Γ— 10⁹⁹(100-digit number)
35455431473961288903…04097900282378321919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.545 Γ— 10⁹⁹(100-digit number)
35455431473961288903…04097900282378321921
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
7.091 Γ— 10⁹⁹(100-digit number)
70910862947922577806…08195800564756643839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.091 Γ— 10⁹⁹(100-digit number)
70910862947922577806…08195800564756643841
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 3850453

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 6c1d5b0344086d9e264ffc4334d8ec98c245902f939d76297ab4ea598e9a4eaa

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 #3,850,453 on Chainz β†—
Circulating Supply:57,975,036 XPMΒ·at block #6,841,333 Β· updates every 60s
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