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Block #56,853

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/17/2013, 10:36:27 AM Β· Difficulty 8.9512 Β· 6,768,699 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
47db7c24ece5ea5aaffaa9a32912ec54f1b95e02746665db795dd90d2082f729
View on Chainz β†—

Height

#56,853

Difficulty

8.951228

Transactions

1

Size

199 B

Version

2

Bits

08f383aa

Nonce

439

Timestamp

7/17/2013, 10:36:27 AM

Confirmations

6,768,699

Merkle Root

c0184b013bbbffce2e7d98b76d68b36cb0ad95ee390b9f1fc9fa3acac4007c4a
Transactions (1)
Coinbasec0184b013bbbff…fa3acac4007c4a
1 in β†’ 1 out12.4600 XPM110 B
ATK8PNcS…XGcPmYeP
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.

3.434 Γ— 10⁹³(94-digit number)
34343541580665772835…73109052594858710700
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
3.434 Γ— 10⁹³(94-digit number)
34343541580665772835…73109052594858710699
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.434 Γ— 10⁹³(94-digit number)
34343541580665772835…73109052594858710701
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
6.868 Γ— 10⁹³(94-digit number)
68687083161331545670…46218105189717421399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.868 Γ— 10⁹³(94-digit number)
68687083161331545670…46218105189717421401
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
1.373 Γ— 10⁹⁴(95-digit number)
13737416632266309134…92436210379434842799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.373 Γ— 10⁹⁴(95-digit number)
13737416632266309134…92436210379434842801
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
2.747 Γ— 10⁹⁴(95-digit number)
27474833264532618268…84872420758869685599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.747 Γ— 10⁹⁴(95-digit number)
27474833264532618268…84872420758869685601
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
5.494 Γ— 10⁹⁴(95-digit number)
54949666529065236536…69744841517739371199
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 56853

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 47db7c24ece5ea5aaffaa9a32912ec54f1b95e02746665db795dd90d2082f729

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 #56,853 on Chainz β†—
Circulating Supply:57,848,517 XPMΒ·at block #6,825,551 Β· updates every 60s
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