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Block #246,299

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/6/2013, 12:48:39 AM Β· Difficulty 9.9644 Β· 6,552,890 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0dacabfbd3752d128e989b097533ebec97515b5dc462b2548d85ff4e82b45c94
View on Chainz β†—

Height

#246,299

Difficulty

9.964359

Transactions

1

Size

209 B

Version

2

Bits

09f6e03f

Nonce

481

Timestamp

11/6/2013, 12:48:39 AM

Confirmations

6,552,890

Merkle Root

b00ba466344d20efe421d9eab85ad8e008adb47d2b14b4911fcbf033208e7277
Transactions (1)
Coinbaseb00ba466344d20…cbf033208e7277
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.

6.990 Γ— 10¹⁰¹(102-digit number)
69906464013385595523…60807978973580492800
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
6.990 Γ— 10¹⁰¹(102-digit number)
69906464013385595523…60807978973580492799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.990 Γ— 10¹⁰¹(102-digit number)
69906464013385595523…60807978973580492801
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
1.398 Γ— 10¹⁰²(103-digit number)
13981292802677119104…21615957947160985599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.398 Γ— 10¹⁰²(103-digit number)
13981292802677119104…21615957947160985601
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
2.796 Γ— 10¹⁰²(103-digit number)
27962585605354238209…43231915894321971199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.796 Γ— 10¹⁰²(103-digit number)
27962585605354238209…43231915894321971201
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
5.592 Γ— 10¹⁰²(103-digit number)
55925171210708476418…86463831788643942399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.592 Γ— 10¹⁰²(103-digit number)
55925171210708476418…86463831788643942401
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
1.118 Γ— 10¹⁰³(104-digit number)
11185034242141695283…72927663577287884799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.118 Γ— 10¹⁰³(104-digit number)
11185034242141695283…72927663577287884801
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 246299

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 0dacabfbd3752d128e989b097533ebec97515b5dc462b2548d85ff4e82b45c94

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 #246,299 on Chainz β†—
Circulating Supply:57,637,550 XPMΒ·at block #6,799,188 Β· updates every 60s
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