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Home/Chain Registry/Block #1,501,993

Block #1,501,993

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/18/2016, 11:04:09 AM Β· Difficulty 10.6426 Β· 5,329,262 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
45a7b4f34b2fe154f5838d953bc563c6d450d74a17d175eac4c23b27b27f7924
View on Chainz β†—

Difficulty

10.642646

Transactions

1

Size

200 B

Version

2

Bits

0aa4847a

Nonce

870,330,780

Timestamp

3/18/2016, 11:04:09 AM

Confirmations

5,329,262

Merkle Root

77bdacecfe865c60fde07480d1c19ac28a9315317e0ad656cfac69af4b3e8046
Transactions (1)
Coinbase77bdacecfe865c…ac69af4b3e8046
1 in β†’ 1 out8.8100 XPM110 B
AGmFQaF8…ATXwC3C1
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.

6.019 Γ— 10⁹⁴(95-digit number)
60197682062546509461…54718536203662645760
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
6.019 Γ— 10⁹⁴(95-digit number)
60197682062546509461…54718536203662645759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.019 Γ— 10⁹⁴(95-digit number)
60197682062546509461…54718536203662645761
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
1.203 Γ— 10⁹⁡(96-digit number)
12039536412509301892…09437072407325291519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.203 Γ— 10⁹⁡(96-digit number)
12039536412509301892…09437072407325291521
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
2.407 Γ— 10⁹⁡(96-digit number)
24079072825018603784…18874144814650583039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.407 Γ— 10⁹⁡(96-digit number)
24079072825018603784…18874144814650583041
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
4.815 Γ— 10⁹⁡(96-digit number)
48158145650037207569…37748289629301166079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.815 Γ— 10⁹⁡(96-digit number)
48158145650037207569…37748289629301166081
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
9.631 Γ— 10⁹⁡(96-digit number)
96316291300074415138…75496579258602332159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.631 Γ— 10⁹⁡(96-digit number)
96316291300074415138…75496579258602332161
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 1501993

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 45a7b4f34b2fe154f5838d953bc563c6d450d74a17d175eac4c23b27b27f7924

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 #1,501,993 on Chainz β†—
Circulating Supply:57,894,190 XPMΒ·at block #6,831,254 Β· updates every 60s
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