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Home/Chain Registry/Block #1,450,962

Block #1,450,962

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/10/2016, 7:51:01 PM Β· Difficulty 10.7443 Β· 5,365,517 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
28ff2139ef71bfe640a9439d3a0d15e0372c8954b1c7496c4beeb55d644d9fa8
View on Chainz β†—

Difficulty

10.744340

Transactions

1

Size

201 B

Version

2

Bits

0abe8d18

Nonce

92,611,301

Timestamp

2/10/2016, 7:51:01 PM

Confirmations

5,365,517

Merkle Root

1c49d791eec5a77dbcece58dd76c8bae90033bc9ad25d9a1ff14f533f2f84249
Transactions (1)
Coinbase1c49d791eec5a7…14f533f2f84249
1 in β†’ 1 out8.6500 XPM110 B
AGmELzN8…L4zgU9mZ
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.

1.340 Γ— 10⁹⁸(99-digit number)
13407070187616203195…63048870835052707840
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
1.340 Γ— 10⁹⁸(99-digit number)
13407070187616203195…63048870835052707839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.340 Γ— 10⁹⁸(99-digit number)
13407070187616203195…63048870835052707841
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
2.681 Γ— 10⁹⁸(99-digit number)
26814140375232406391…26097741670105415679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.681 Γ— 10⁹⁸(99-digit number)
26814140375232406391…26097741670105415681
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
5.362 Γ— 10⁹⁸(99-digit number)
53628280750464812782…52195483340210831359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.362 Γ— 10⁹⁸(99-digit number)
53628280750464812782…52195483340210831361
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
1.072 Γ— 10⁹⁹(100-digit number)
10725656150092962556…04390966680421662719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.072 Γ— 10⁹⁹(100-digit number)
10725656150092962556…04390966680421662721
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
2.145 Γ— 10⁹⁹(100-digit number)
21451312300185925113…08781933360843325439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.145 Γ— 10⁹⁹(100-digit number)
21451312300185925113…08781933360843325441
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 1450962

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 28ff2139ef71bfe640a9439d3a0d15e0372c8954b1c7496c4beeb55d644d9fa8

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 #1,450,962 on Chainz β†—
Circulating Supply:57,775,962 XPMΒ·at block #6,816,478 Β· updates every 60s
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