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Home/Chain Registry/Block #1,597,301

Block #1,597,301

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/23/2016, 11:44:36 PM Β· Difficulty 10.6110 Β· 5,229,781 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5a3bee9bac2f09f0828a451f28a8a2435e4e5eb9c9c34cc8282aa586fc2c5a18
View on Chainz β†—

Difficulty

10.610956

Transactions

1

Size

243 B

Version

2

Bits

0a9c6798

Nonce

1,133,494,083

Timestamp

5/23/2016, 11:44:36 PM

Confirmations

5,229,781

Merkle Root

09c586327b1a284d875dbcab813f1e175583283ee4c46981ef72eb1cc746361d
Transactions (1)
Coinbase09c586327b1a28…72eb1cc746361d
1 in β†’ 2 out8.8700 XPM152 B
AW7XpJLz…npEJgCfvALPu3s2c…EJXLjVFh
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.

3.958 Γ— 10⁹⁢(97-digit number)
39584292309997758280…08100748678781497600
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
3.958 Γ— 10⁹⁢(97-digit number)
39584292309997758280…08100748678781497599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.958 Γ— 10⁹⁢(97-digit number)
39584292309997758280…08100748678781497601
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
7.916 Γ— 10⁹⁢(97-digit number)
79168584619995516560…16201497357562995199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.916 Γ— 10⁹⁢(97-digit number)
79168584619995516560…16201497357562995201
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
1.583 Γ— 10⁹⁷(98-digit number)
15833716923999103312…32402994715125990399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.583 Γ— 10⁹⁷(98-digit number)
15833716923999103312…32402994715125990401
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
3.166 Γ— 10⁹⁷(98-digit number)
31667433847998206624…64805989430251980799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.166 Γ— 10⁹⁷(98-digit number)
31667433847998206624…64805989430251980801
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
6.333 Γ— 10⁹⁷(98-digit number)
63334867695996413248…29611978860503961599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.333 Γ— 10⁹⁷(98-digit number)
63334867695996413248…29611978860503961601
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 1597301

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 5a3bee9bac2f09f0828a451f28a8a2435e4e5eb9c9c34cc8282aa586fc2c5a18

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 #1,597,301 on Chainz β†—
Circulating Supply:57,860,841 XPMΒ·at block #6,827,081 Β· updates every 60s
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