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Block #246,855

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/6/2013, 9:57:57 AM Β· Difficulty 9.9644 Β· 6,558,138 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4e1a685c18caf8b8174d3841e5d85ac5605a5407dc44fa28fa809db8ee4f0f6f
View on Chainz β†—

Height

#246,855

Difficulty

9.964449

Transactions

1

Size

207 B

Version

2

Bits

09f6e624

Nonce

2,515

Timestamp

11/6/2013, 9:57:57 AM

Confirmations

6,558,138

Merkle Root

dc43cea4a6efab226a6369ba0717409bda3bdcaa06ee7b58d71cad8e456ea1b6
Transactions (1)
Coinbasedc43cea4a6efab…1cad8e456ea1b6
1 in β†’ 1 out10.0600 XPM116 B
AcLBm5Z9…S683d7c3
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.

7.618 Γ— 10⁹⁢(97-digit number)
76186926124903968213…75761928745098795000
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
7.618 Γ— 10⁹⁢(97-digit number)
76186926124903968213…75761928745098794999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.618 Γ— 10⁹⁢(97-digit number)
76186926124903968213…75761928745098795001
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
1.523 Γ— 10⁹⁷(98-digit number)
15237385224980793642…51523857490197589999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.523 Γ— 10⁹⁷(98-digit number)
15237385224980793642…51523857490197590001
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
3.047 Γ— 10⁹⁷(98-digit number)
30474770449961587285…03047714980395179999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.047 Γ— 10⁹⁷(98-digit number)
30474770449961587285…03047714980395180001
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
6.094 Γ— 10⁹⁷(98-digit number)
60949540899923174570…06095429960790359999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.094 Γ— 10⁹⁷(98-digit number)
60949540899923174570…06095429960790360001
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
1.218 Γ— 10⁹⁸(99-digit number)
12189908179984634914…12190859921580719999
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 246855

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 4e1a685c18caf8b8174d3841e5d85ac5605a5407dc44fa28fa809db8ee4f0f6f

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 #246,855 on Chainz β†—
Circulating Supply:57,684,014 XPMΒ·at block #6,804,992 Β· updates every 60s
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