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Block #307,008

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/12/2013, 8:51:18 AM Β· Difficulty 9.9940 Β· 6,496,954 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f49e3e532012f2b98d7c92f4b15e73122864d8a899b5e2612a49bda1a12a6aeb
View on Chainz β†—

Height

#307,008

Difficulty

9.994048

Transactions

1

Size

208 B

Version

2

Bits

09fe79e6

Nonce

107,402

Timestamp

12/12/2013, 8:51:18 AM

Confirmations

6,496,954

Merkle Root

51cb622674e4446d85169b4fbd0ff490d950178da86786ec7db2bbe8274c811f
Transactions (1)
Coinbase51cb622674e444…b2bbe8274c811f
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.

1.674 Γ— 10⁹⁹(100-digit number)
16744269922959719595…67358888428137856000
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
1.674 Γ— 10⁹⁹(100-digit number)
16744269922959719595…67358888428137855999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.674 Γ— 10⁹⁹(100-digit number)
16744269922959719595…67358888428137856001
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
3.348 Γ— 10⁹⁹(100-digit number)
33488539845919439191…34717776856275711999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.348 Γ— 10⁹⁹(100-digit number)
33488539845919439191…34717776856275712001
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
6.697 Γ— 10⁹⁹(100-digit number)
66977079691838878383…69435553712551423999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.697 Γ— 10⁹⁹(100-digit number)
66977079691838878383…69435553712551424001
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
1.339 Γ— 10¹⁰⁰(101-digit number)
13395415938367775676…38871107425102847999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.339 Γ— 10¹⁰⁰(101-digit number)
13395415938367775676…38871107425102848001
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
2.679 Γ— 10¹⁰⁰(101-digit number)
26790831876735551353…77742214850205695999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.679 Γ— 10¹⁰⁰(101-digit number)
26790831876735551353…77742214850205696001
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 307008

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 f49e3e532012f2b98d7c92f4b15e73122864d8a899b5e2612a49bda1a12a6aeb

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 #307,008 on Chainz β†—
Circulating Supply:57,675,748 XPMΒ·at block #6,803,961 Β· updates every 60s
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