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Home/Chain Registry/Block #3,504,865

Block #3,504,865

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/8/2020, 5:28:32 AM Β· Difficulty 10.9306 Β· 3,327,762 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fa60c374455c9ec84733f58e08f10a0099c1eedc04b5eaa40366ab814af177e2
View on Chainz β†—

Difficulty

10.930596

Transactions

2

Size

7.45 KB

Version

2

Bits

0aee3b8d

Nonce

1,314,408,068

Timestamp

1/8/2020, 5:28:32 AM

Confirmations

3,327,762

Merkle Root

583405600618e2affaa6eb7a0650399c7ea04f0e966cd748a830b6aed8dc341f
Transactions (2)
Coinbase8e446795ee8557…563992daf69c10
1 in β†’ 1 out8.4400 XPM109 B
AXfJqzUb…HXeXmjMz
69efa102b43284…ce8b30e59ed919
50 in β†’ 1 out199.9200 XPM7.26 KB
ALcTQaSP…1C5Yf2Zi
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.

2.905 Γ— 10⁹⁷(98-digit number)
29057793483064623472…61287047566394035200
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
2.905 Γ— 10⁹⁷(98-digit number)
29057793483064623472…61287047566394035199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.905 Γ— 10⁹⁷(98-digit number)
29057793483064623472…61287047566394035201
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
5.811 Γ— 10⁹⁷(98-digit number)
58115586966129246945…22574095132788070399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.811 Γ— 10⁹⁷(98-digit number)
58115586966129246945…22574095132788070401
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
1.162 Γ— 10⁹⁸(99-digit number)
11623117393225849389…45148190265576140799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.162 Γ— 10⁹⁸(99-digit number)
11623117393225849389…45148190265576140801
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
2.324 Γ— 10⁹⁸(99-digit number)
23246234786451698778…90296380531152281599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.324 Γ— 10⁹⁸(99-digit number)
23246234786451698778…90296380531152281601
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
4.649 Γ— 10⁹⁸(99-digit number)
46492469572903397556…80592761062304563199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.649 Γ— 10⁹⁸(99-digit number)
46492469572903397556…80592761062304563201
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 3504865

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 fa60c374455c9ec84733f58e08f10a0099c1eedc04b5eaa40366ab814af177e2

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 #3,504,865 on Chainz β†—
Circulating Supply:57,905,164 XPMΒ·at block #6,832,626 Β· updates every 60s
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