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Block #316,745

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/17/2013, 6:12:11 AM Β· Difficulty 10.1436 Β· 6,478,082 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1deb23085c24264bd2aeca5336769ac71a26ee3450698bf3b3bc7b314508a8d3
View on Chainz β†—

Height

#316,745

Difficulty

10.143641

Transactions

1

Size

210 B

Version

2

Bits

0a24c5aa

Nonce

7,959

Timestamp

12/17/2013, 6:12:11 AM

Confirmations

6,478,082

Merkle Root

5d41242e40f90e4835176e553a74fcc2c97298fa9d2a62e609b2a67813639a23
Transactions (1)
Coinbase5d41242e40f90e…b2a67813639a23
1 in β†’ 1 out9.7000 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.

3.994 Γ— 10¹⁰³(104-digit number)
39946096260072221857…23761075136873382400
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
3.994 Γ— 10¹⁰³(104-digit number)
39946096260072221857…23761075136873382399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.994 Γ— 10¹⁰³(104-digit number)
39946096260072221857…23761075136873382401
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
7.989 Γ— 10¹⁰³(104-digit number)
79892192520144443714…47522150273746764799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.989 Γ— 10¹⁰³(104-digit number)
79892192520144443714…47522150273746764801
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
1.597 Γ— 10¹⁰⁴(105-digit number)
15978438504028888742…95044300547493529599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.597 Γ— 10¹⁰⁴(105-digit number)
15978438504028888742…95044300547493529601
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
3.195 Γ— 10¹⁰⁴(105-digit number)
31956877008057777485…90088601094987059199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.195 Γ— 10¹⁰⁴(105-digit number)
31956877008057777485…90088601094987059201
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
6.391 Γ— 10¹⁰⁴(105-digit number)
63913754016115554971…80177202189974118399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.391 Γ— 10¹⁰⁴(105-digit number)
63913754016115554971…80177202189974118401
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 316745

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 1deb23085c24264bd2aeca5336769ac71a26ee3450698bf3b3bc7b314508a8d3

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 #316,745 on Chainz β†—
Circulating Supply:57,602,665 XPMΒ·at block #6,794,826 Β· updates every 60s
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