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Home/Chain Registry/Block #1,524,390

Block #1,524,390

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/3/2016, 10:01:35 AM Β· Difficulty 10.5999 Β· 5,302,394 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0c40dc61bafd14a9e056b7c9b983d67b10c3361713997f826ee7d268cb95715d
View on Chainz β†—

Difficulty

10.599920

Transactions

1

Size

199 B

Version

2

Bits

0a99945a

Nonce

1,506,373,593

Timestamp

4/3/2016, 10:01:35 AM

Confirmations

5,302,394

Merkle Root

2dfa468137f79d8a7b8f482d749ec24303c14a7b11627bb765d71a0eb4daf776
Transactions (1)
Coinbase2dfa468137f79d…d71a0eb4daf776
1 in β†’ 1 out8.8900 XPM109 B
AN7iDnRr…xPQayPcm
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.

9.136 Γ— 10⁹⁴(95-digit number)
91368850529227102399…09901761539175707520
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
9.136 Γ— 10⁹⁴(95-digit number)
91368850529227102399…09901761539175707519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.136 Γ— 10⁹⁴(95-digit number)
91368850529227102399…09901761539175707521
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
1.827 Γ— 10⁹⁡(96-digit number)
18273770105845420479…19803523078351415039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.827 Γ— 10⁹⁡(96-digit number)
18273770105845420479…19803523078351415041
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
3.654 Γ— 10⁹⁡(96-digit number)
36547540211690840959…39607046156702830079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.654 Γ— 10⁹⁡(96-digit number)
36547540211690840959…39607046156702830081
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
7.309 Γ— 10⁹⁡(96-digit number)
73095080423381681919…79214092313405660159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.309 Γ— 10⁹⁡(96-digit number)
73095080423381681919…79214092313405660161
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
1.461 Γ— 10⁹⁢(97-digit number)
14619016084676336383…58428184626811320319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.461 Γ— 10⁹⁢(97-digit number)
14619016084676336383…58428184626811320321
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 1524390

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 0c40dc61bafd14a9e056b7c9b983d67b10c3361713997f826ee7d268cb95715d

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 #1,524,390 on Chainz β†—
Circulating Supply:57,858,432 XPMΒ·at block #6,826,783 Β· updates every 60s
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