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Home/Chain Registry/Block #2,234,621

Block #2,234,621

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/3/2017, 4:00:51 AM Β· Difficulty 10.9457 Β· 4,592,700 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
56c9e90034ca754e09d68cecd5ed1eb5c8b8f1ce9aae6b43899edd3c3ee6ef01
View on Chainz β†—

Difficulty

10.945702

Transactions

2

Size

393 B

Version

2

Bits

0af21980

Nonce

1,754,866,662

Timestamp

8/3/2017, 4:00:51 AM

Confirmations

4,592,700

Merkle Root

dd5bb3b1c8a2672ef89fd0ff5ce5e8a35bb1417b7ee72dc76528aaa551326507
Transactions (2)
Coinbase0f8db42be02bad…990116122c63b9
1 in β†’ 1 out8.3400 XPM110 B
AUmzqQM4…hbWRxuRy
d7401bc5ff9fc8…edfc67855fa926
1 in β†’ 2 out8.3200 XPM193 B
AKPyzYuG…66TS33LNASdXKexa…kch59HW5
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.

1.475 Γ— 10⁹⁴(95-digit number)
14757576048546267956…90285935690319718480
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
1.475 Γ— 10⁹⁴(95-digit number)
14757576048546267956…90285935690319718479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.475 Γ— 10⁹⁴(95-digit number)
14757576048546267956…90285935690319718481
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
2.951 Γ— 10⁹⁴(95-digit number)
29515152097092535912…80571871380639436959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.951 Γ— 10⁹⁴(95-digit number)
29515152097092535912…80571871380639436961
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
5.903 Γ— 10⁹⁴(95-digit number)
59030304194185071824…61143742761278873919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.903 Γ— 10⁹⁴(95-digit number)
59030304194185071824…61143742761278873921
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
1.180 Γ— 10⁹⁡(96-digit number)
11806060838837014364…22287485522557747839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.180 Γ— 10⁹⁡(96-digit number)
11806060838837014364…22287485522557747841
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
2.361 Γ— 10⁹⁡(96-digit number)
23612121677674028729…44574971045115495679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.361 Γ— 10⁹⁡(96-digit number)
23612121677674028729…44574971045115495681
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 2234621

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 56c9e90034ca754e09d68cecd5ed1eb5c8b8f1ce9aae6b43899edd3c3ee6ef01

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 #2,234,621 on Chainz β†—
Circulating Supply:57,862,680 XPMΒ·at block #6,827,320 Β· updates every 60s
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