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Block #57,449

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/17/2013, 2:37:23 PM Β· Difficulty 8.9546 Β· 6,749,989 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6ff5caec14b0aae3efab312a4ef6e059e69f11d5438aa1798f9ccc2c44d14b1c
View on Chainz β†—

Height

#57,449

Difficulty

8.954572

Transactions

1

Size

198 B

Version

2

Bits

08f45ed0

Nonce

9

Timestamp

7/17/2013, 2:37:23 PM

Confirmations

6,749,989

Merkle Root

12748f8dcc769f5af8638c8580e4affbe07293b687642b5c9d2653b5828a96b5
Transactions (1)
Coinbase12748f8dcc769f…2653b5828a96b5
1 in β†’ 1 out12.4500 XPM110 B
AJSbceEa…M6r1P32t
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.

4.599 Γ— 10⁸⁸(89-digit number)
45993893773311812982…08814237827177838530
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
4.599 Γ— 10⁸⁸(89-digit number)
45993893773311812982…08814237827177838529
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.599 Γ— 10⁸⁸(89-digit number)
45993893773311812982…08814237827177838531
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
9.198 Γ— 10⁸⁸(89-digit number)
91987787546623625964…17628475654355677059
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.198 Γ— 10⁸⁸(89-digit number)
91987787546623625964…17628475654355677061
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
1.839 Γ— 10⁸⁹(90-digit number)
18397557509324725192…35256951308711354119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.839 Γ— 10⁸⁹(90-digit number)
18397557509324725192…35256951308711354121
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
3.679 Γ— 10⁸⁹(90-digit number)
36795115018649450385…70513902617422708239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.679 Γ— 10⁸⁹(90-digit number)
36795115018649450385…70513902617422708241
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
7.359 Γ— 10⁸⁹(90-digit number)
73590230037298900771…41027805234845416479
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 57449

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 6ff5caec14b0aae3efab312a4ef6e059e69f11d5438aa1798f9ccc2c44d14b1c

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 #57,449 on Chainz β†—
Circulating Supply:57,703,527 XPMΒ·at block #6,807,437 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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