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Block #312,391

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/15/2013, 12:05:44 AM Β· Difficulty 9.9958 Β· 6,484,091 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b7b9f61ffeeecb0345e7485f1e86d80e709cbbf87757895ca533b4a984f26402
View on Chainz β†—

Height

#312,391

Difficulty

9.995801

Transactions

2

Size

869 B

Version

2

Bits

09feecd0

Nonce

80,518

Timestamp

12/15/2013, 12:05:44 AM

Confirmations

6,484,091

Merkle Root

eda4309c3289d68ea142122d00f07bbf8ba5d8f6f5f4bcd6384d63494cec3c0f
Transactions (2)
Coinbase6d9e884151c298…173c41a5987beb
1 in β†’ 1 out10.0000 XPM110 B
AeKNrjNj…1NEq95Ta
66a21f39fe8e6c…05d83e1d9a281d
4 in β†’ 2 out1.1475 XPM668 B
AYWRFUvM…x7bwVE4cAeaYHHSp…p95h5oia
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.

5.233 Γ— 10⁹⁷(98-digit number)
52339806431644234772…98939793639374295040
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
5.233 Γ— 10⁹⁷(98-digit number)
52339806431644234772…98939793639374295039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.233 Γ— 10⁹⁷(98-digit number)
52339806431644234772…98939793639374295041
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
1.046 Γ— 10⁹⁸(99-digit number)
10467961286328846954…97879587278748590079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.046 Γ— 10⁹⁸(99-digit number)
10467961286328846954…97879587278748590081
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
2.093 Γ— 10⁹⁸(99-digit number)
20935922572657693908…95759174557497180159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.093 Γ— 10⁹⁸(99-digit number)
20935922572657693908…95759174557497180161
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
4.187 Γ— 10⁹⁸(99-digit number)
41871845145315387817…91518349114994360319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.187 Γ— 10⁹⁸(99-digit number)
41871845145315387817…91518349114994360321
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
8.374 Γ— 10⁹⁸(99-digit number)
83743690290630775635…83036698229988720639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.374 Γ— 10⁹⁸(99-digit number)
83743690290630775635…83036698229988720641
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 312391

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 b7b9f61ffeeecb0345e7485f1e86d80e709cbbf87757895ca533b4a984f26402

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 #312,391 on Chainz β†—
Circulating Supply:57,615,856 XPMΒ·at block #6,796,481 Β· updates every 60s
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