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Home/Chain Registry/Block #1,597,949

Block #1,597,949

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/24/2016, 10:47:29 AM Β· Difficulty 10.6098 Β· 5,245,300 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
44726720a8515f35604a38c9aefe9f0078b8265d26e6a291d48952148b569c7b
View on Chainz β†—

Difficulty

10.609847

Transactions

1

Size

200 B

Version

2

Bits

0a9c1eef

Nonce

742,864,158

Timestamp

5/24/2016, 10:47:29 AM

Confirmations

5,245,300

Merkle Root

1e949196a6ba2140b57557c10460b80f091ae24cc2a2f38d69e9774b6ed72917
Transactions (1)
Coinbase1e949196a6ba21…e9774b6ed72917
1 in β†’ 1 out8.8700 XPM109 B
AUCGK4M7…bBbnGgQ5
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.

1.093 Γ— 10⁹⁸(99-digit number)
10930001860262721365…04740133437513072640
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
1.093 Γ— 10⁹⁸(99-digit number)
10930001860262721365…04740133437513072639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.093 Γ— 10⁹⁸(99-digit number)
10930001860262721365…04740133437513072641
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
2.186 Γ— 10⁹⁸(99-digit number)
21860003720525442731…09480266875026145279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.186 Γ— 10⁹⁸(99-digit number)
21860003720525442731…09480266875026145281
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
4.372 Γ— 10⁹⁸(99-digit number)
43720007441050885462…18960533750052290559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.372 Γ— 10⁹⁸(99-digit number)
43720007441050885462…18960533750052290561
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
8.744 Γ— 10⁹⁸(99-digit number)
87440014882101770924…37921067500104581119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.744 Γ— 10⁹⁸(99-digit number)
87440014882101770924…37921067500104581121
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
1.748 Γ— 10⁹⁹(100-digit number)
17488002976420354184…75842135000209162239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.748 Γ— 10⁹⁹(100-digit number)
17488002976420354184…75842135000209162241
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 1597949

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 44726720a8515f35604a38c9aefe9f0078b8265d26e6a291d48952148b569c7b

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 #1,597,949 on Chainz β†—
Circulating Supply:57,990,368 XPMΒ·at block #6,843,248 Β· updates every 60s
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