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Block #318,354

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/18/2013, 7:30:10 AM Β· Difficulty 10.1595 Β· 6,482,664 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
862d9a977a3cd8186340ba3e7dd6cc7d128c5fb17409ef5d0fb54f2facf678ef
View on Chainz β†—

Height

#318,354

Difficulty

10.159476

Transactions

1

Size

207 B

Version

2

Bits

0a28d36c

Nonce

424,302

Timestamp

12/18/2013, 7:30:10 AM

Confirmations

6,482,664

Merkle Root

427fe60863d1507b607582959f14fd1e9635808c4d1fc1e51f2964fea860f911
Transactions (1)
Coinbase427fe60863d150…2964fea860f911
1 in β†’ 1 out9.6700 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.

1.200 Γ— 10⁹⁷(98-digit number)
12005272981420520623…60409336640507796480
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
1.200 Γ— 10⁹⁷(98-digit number)
12005272981420520623…60409336640507796479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.200 Γ— 10⁹⁷(98-digit number)
12005272981420520623…60409336640507796481
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
2.401 Γ— 10⁹⁷(98-digit number)
24010545962841041246…20818673281015592959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.401 Γ— 10⁹⁷(98-digit number)
24010545962841041246…20818673281015592961
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
4.802 Γ— 10⁹⁷(98-digit number)
48021091925682082493…41637346562031185919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.802 Γ— 10⁹⁷(98-digit number)
48021091925682082493…41637346562031185921
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
9.604 Γ— 10⁹⁷(98-digit number)
96042183851364164986…83274693124062371839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.604 Γ— 10⁹⁷(98-digit number)
96042183851364164986…83274693124062371841
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
1.920 Γ— 10⁹⁸(99-digit number)
19208436770272832997…66549386248124743679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.920 Γ— 10⁹⁸(99-digit number)
19208436770272832997…66549386248124743681
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 318354

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 862d9a977a3cd8186340ba3e7dd6cc7d128c5fb17409ef5d0fb54f2facf678ef

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 #318,354 on Chainz β†—
Circulating Supply:57,652,206 XPMΒ·at block #6,801,017 Β· updates every 60s
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