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Block #308,316

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/13/2013, 1:21:35 AM Β· Difficulty 9.9945 Β· 6,516,400 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
66f437180e0735ccd2871e941bbd99ee3b864bc9f51c3e29a6d3bc63b3a9913b
View on Chainz β†—

Height

#308,316

Difficulty

9.994451

Transactions

1

Size

207 B

Version

2

Bits

09fe945d

Nonce

60,144

Timestamp

12/13/2013, 1:21:35 AM

Confirmations

6,516,400

Merkle Root

81c94bd0d310db4a7371bdc1ed2154be928236ce50328d97f593462e56194c70
Transactions (1)
Coinbase81c94bd0d310db…93462e56194c70
1 in β†’ 1 out10.0000 XPM116 B
AbwWkWZt…kawDhufa
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.

7.561 Γ— 10⁹⁷(98-digit number)
75611458530577951671…76956302830920486720
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
7.561 Γ— 10⁹⁷(98-digit number)
75611458530577951671…76956302830920486719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.561 Γ— 10⁹⁷(98-digit number)
75611458530577951671…76956302830920486721
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
1.512 Γ— 10⁹⁸(99-digit number)
15122291706115590334…53912605661840973439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.512 Γ— 10⁹⁸(99-digit number)
15122291706115590334…53912605661840973441
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
3.024 Γ— 10⁹⁸(99-digit number)
30244583412231180668…07825211323681946879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.024 Γ— 10⁹⁸(99-digit number)
30244583412231180668…07825211323681946881
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
6.048 Γ— 10⁹⁸(99-digit number)
60489166824462361337…15650422647363893759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.048 Γ— 10⁹⁸(99-digit number)
60489166824462361337…15650422647363893761
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
1.209 Γ— 10⁹⁹(100-digit number)
12097833364892472267…31300845294727787519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.209 Γ— 10⁹⁹(100-digit number)
12097833364892472267…31300845294727787521
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 308316

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 66f437180e0735ccd2871e941bbd99ee3b864bc9f51c3e29a6d3bc63b3a9913b

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 #308,316 on Chainz β†—
Circulating Supply:57,841,794 XPMΒ·at block #6,824,715 Β· updates every 60s
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