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Block #315,507

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/16/2013, 1:22:41 PM Β· Difficulty 10.1035 Β· 6,479,942 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3a32c307d80c65e66bb4487be156c2256ec77de79b5faf6c87611bc841de9934
View on Chainz β†—

Height

#315,507

Difficulty

10.103516

Transactions

1

Size

201 B

Version

2

Bits

0a1a8000

Nonce

5,968

Timestamp

12/16/2013, 1:22:41 PM

Confirmations

6,479,942

Merkle Root

669f05bc0a97b6003ae14b9ac307c6324c0762d87729d699fa3f3a0cca71a456
Transactions (1)
Coinbase669f05bc0a97b6…3f3a0cca71a456
1 in β†’ 1 out9.7800 XPM109 B
AZ8EXFCa…yj4u4dvd
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.

1.127 Γ— 10⁹⁹(100-digit number)
11278379717539099593…52764655602435537920
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
1.127 Γ— 10⁹⁹(100-digit number)
11278379717539099593…52764655602435537919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.127 Γ— 10⁹⁹(100-digit number)
11278379717539099593…52764655602435537921
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
2.255 Γ— 10⁹⁹(100-digit number)
22556759435078199187…05529311204871075839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.255 Γ— 10⁹⁹(100-digit number)
22556759435078199187…05529311204871075841
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
4.511 Γ— 10⁹⁹(100-digit number)
45113518870156398374…11058622409742151679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.511 Γ— 10⁹⁹(100-digit number)
45113518870156398374…11058622409742151681
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
9.022 Γ— 10⁹⁹(100-digit number)
90227037740312796749…22117244819484303359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.022 Γ— 10⁹⁹(100-digit number)
90227037740312796749…22117244819484303361
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
1.804 Γ— 10¹⁰⁰(101-digit number)
18045407548062559349…44234489638968606719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.804 Γ— 10¹⁰⁰(101-digit number)
18045407548062559349…44234489638968606721
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 315507

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 3a32c307d80c65e66bb4487be156c2256ec77de79b5faf6c87611bc841de9934

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 #315,507 on Chainz β†—
Circulating Supply:57,607,658 XPMΒ·at block #6,795,448 Β· updates every 60s
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