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Block #316,395

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/17/2013, 1:21:12 AM Β· Difficulty 10.1334 Β· 6,508,263 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ac616ff224f9f485c667aaffc98d528de29203686b240b558eaf39835c0b70bc
View on Chainz β†—

Height

#316,395

Difficulty

10.133448

Transactions

1

Size

201 B

Version

2

Bits

0a22299e

Nonce

22,664

Timestamp

12/17/2013, 1:21:12 AM

Confirmations

6,508,263

Merkle Root

2c5ffc89e71c6d3e6b1988c3941406a80d1515316cd754262ffe076548c92239
Transactions (1)
Coinbase2c5ffc89e71c6d…fe076548c92239
1 in β†’ 1 out9.7200 XPM109 B
AekRpo1N…i7TZgss9
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.

1.101 Γ— 10⁹⁹(100-digit number)
11015544742960124581…40361799823128217600
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
1.101 Γ— 10⁹⁹(100-digit number)
11015544742960124581…40361799823128217599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.101 Γ— 10⁹⁹(100-digit number)
11015544742960124581…40361799823128217601
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
2.203 Γ— 10⁹⁹(100-digit number)
22031089485920249163…80723599646256435199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.203 Γ— 10⁹⁹(100-digit number)
22031089485920249163…80723599646256435201
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
4.406 Γ— 10⁹⁹(100-digit number)
44062178971840498326…61447199292512870399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.406 Γ— 10⁹⁹(100-digit number)
44062178971840498326…61447199292512870401
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
8.812 Γ— 10⁹⁹(100-digit number)
88124357943680996653…22894398585025740799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.812 Γ— 10⁹⁹(100-digit number)
88124357943680996653…22894398585025740801
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
1.762 Γ— 10¹⁰⁰(101-digit number)
17624871588736199330…45788797170051481599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.762 Γ— 10¹⁰⁰(101-digit number)
17624871588736199330…45788797170051481601
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 316395

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 ac616ff224f9f485c667aaffc98d528de29203686b240b558eaf39835c0b70bc

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 #316,395 on Chainz β†—
Circulating Supply:57,841,329 XPMΒ·at block #6,824,657 Β· updates every 60s
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