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Block #317,749

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/17/2013, 9:54:43 PM Β· Difficulty 10.1548 Β· 6,489,128 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5672309f489d7bd1bbf4bc052d860b72593655dcded5e3df9e843eaaa58ef998
View on Chainz β†—

Height

#317,749

Difficulty

10.154841

Transactions

1

Size

202 B

Version

2

Bits

0a27a3b0

Nonce

253,638

Timestamp

12/17/2013, 9:54:43 PM

Confirmations

6,489,128

Merkle Root

e301234d6d9e876e7760258555d12da1b61f026e698d36301f56d6ccd2350722
Transactions (1)
Coinbasee301234d6d9e87…56d6ccd2350722
1 in β†’ 1 out9.6800 XPM110 B
AeKNrjNj…1NEq95Ta
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.

4.090 Γ— 10⁹⁹(100-digit number)
40900119562411455232…09127862876753168000
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
4.090 Γ— 10⁹⁹(100-digit number)
40900119562411455232…09127862876753167999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.090 Γ— 10⁹⁹(100-digit number)
40900119562411455232…09127862876753168001
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
8.180 Γ— 10⁹⁹(100-digit number)
81800239124822910464…18255725753506335999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.180 Γ— 10⁹⁹(100-digit number)
81800239124822910464…18255725753506336001
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
1.636 Γ— 10¹⁰⁰(101-digit number)
16360047824964582092…36511451507012671999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.636 Γ— 10¹⁰⁰(101-digit number)
16360047824964582092…36511451507012672001
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
3.272 Γ— 10¹⁰⁰(101-digit number)
32720095649929164185…73022903014025343999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.272 Γ— 10¹⁰⁰(101-digit number)
32720095649929164185…73022903014025344001
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
6.544 Γ— 10¹⁰⁰(101-digit number)
65440191299858328371…46045806028050687999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.544 Γ— 10¹⁰⁰(101-digit number)
65440191299858328371…46045806028050688001
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 317749

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 5672309f489d7bd1bbf4bc052d860b72593655dcded5e3df9e843eaaa58ef998

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 #317,749 on Chainz β†—
Circulating Supply:57,699,124 XPMΒ·at block #6,806,876 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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