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Block #306,757

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/12/2013, 5:38:20 AM Β· Difficulty 9.9940 Β· 6,489,243 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f433c9fe5a05797fba103c55396dda81fd4ed52615bb9c8a2b0d5d16ca776ebb
View on Chainz β†—

Height

#306,757

Difficulty

9.993974

Transactions

2

Size

1.57 KB

Version

2

Bits

09fe7518

Nonce

536,477

Timestamp

12/12/2013, 5:38:20 AM

Confirmations

6,489,243

Merkle Root

098ccae256fe3c9904121d1239038ec37418350299acf6b018867661097effc8
Transactions (2)
Coinbasef3d17fcd8a85cb…2aceeaaabd3479
1 in β†’ 1 out10.0200 XPM110 B
AeKNrjNj…1NEq95Ta
d3eb4cec932936…e3895e0e026279
9 in β†’ 2 out9.8313 XPM1.37 KB
AK7L8unH…AiFZjBKqAYSZg2Lm…G2Yq4Veq
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.

2.519 Γ— 10⁹⁷(98-digit number)
25196019348674410321…42247143438220270400
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
2.519 Γ— 10⁹⁷(98-digit number)
25196019348674410321…42247143438220270399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.519 Γ— 10⁹⁷(98-digit number)
25196019348674410321…42247143438220270401
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
5.039 Γ— 10⁹⁷(98-digit number)
50392038697348820643…84494286876440540799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.039 Γ— 10⁹⁷(98-digit number)
50392038697348820643…84494286876440540801
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
1.007 Γ— 10⁹⁸(99-digit number)
10078407739469764128…68988573752881081599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.007 Γ— 10⁹⁸(99-digit number)
10078407739469764128…68988573752881081601
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
2.015 Γ— 10⁹⁸(99-digit number)
20156815478939528257…37977147505762163199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.015 Γ— 10⁹⁸(99-digit number)
20156815478939528257…37977147505762163201
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
4.031 Γ— 10⁹⁸(99-digit number)
40313630957879056514…75954295011524326399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.031 Γ— 10⁹⁸(99-digit number)
40313630957879056514…75954295011524326401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
8.062 Γ— 10⁹⁸(99-digit number)
80627261915758113029…51908590023048652799
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 306757

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 f433c9fe5a05797fba103c55396dda81fd4ed52615bb9c8a2b0d5d16ca776ebb

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 #306,757 on Chainz β†—
Circulating Supply:57,612,090 XPMΒ·at block #6,795,999 Β· updates every 60s
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