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Block #210,776

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/15/2013, 8:47:18 AM Β· Difficulty 9.9136 Β· 6,588,032 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6e02a1ac6abaf85be36e006a5b8a77da2a53926902c7f5c03718cd7ca0561577
View on Chainz β†—

Height

#210,776

Difficulty

9.913571

Transactions

1

Size

198 B

Version

2

Bits

09e9dfc3

Nonce

3,255

Timestamp

10/15/2013, 8:47:18 AM

Confirmations

6,588,032

Merkle Root

d1b0ab9f00ad2d1f9af46c957a3abf2add5869723f7a40b7cf3622f5a6ab4c1f
Transactions (1)
Coinbased1b0ab9f00ad2d…3622f5a6ab4c1f
1 in β†’ 1 out10.1600 XPM109 B
AUhLRPTb…NNfhXYRC
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.

4.628 Γ— 10⁹²(93-digit number)
46281843413565149056…27769988044808662240
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
4.628 Γ— 10⁹²(93-digit number)
46281843413565149056…27769988044808662239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.628 Γ— 10⁹²(93-digit number)
46281843413565149056…27769988044808662241
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
9.256 Γ— 10⁹²(93-digit number)
92563686827130298113…55539976089617324479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.256 Γ— 10⁹²(93-digit number)
92563686827130298113…55539976089617324481
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
1.851 Γ— 10⁹³(94-digit number)
18512737365426059622…11079952179234648959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.851 Γ— 10⁹³(94-digit number)
18512737365426059622…11079952179234648961
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
3.702 Γ— 10⁹³(94-digit number)
37025474730852119245…22159904358469297919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.702 Γ— 10⁹³(94-digit number)
37025474730852119245…22159904358469297921
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
7.405 Γ— 10⁹³(94-digit number)
74050949461704238491…44319808716938595839
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 210776

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 6e02a1ac6abaf85be36e006a5b8a77da2a53926902c7f5c03718cd7ca0561577

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 #210,776 on Chainz β†—
Circulating Supply:57,634,490 XPMΒ·at block #6,798,807 Β· updates every 60s
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