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Block #491,443

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/14/2014, 12:44:50 PM Β· Difficulty 10.6809 Β· 6,334,701 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
92b612ef5e4d8da5c36fdb96033b407032c5eb2546f87897b433b0a35e3ee5b2
View on Chainz β†—

Height

#491,443

Difficulty

10.680907

Transactions

1

Size

208 B

Version

2

Bits

0aae4ff1

Nonce

5,972

Timestamp

4/14/2014, 12:44:50 PM

Confirmations

6,334,701

Merkle Root

5398fd5fb38133072f006dac4566fe138b7d3d23119896457b43728b7bc6be6a
Transactions (1)
Coinbase5398fd5fb38133…43728b7bc6be6a
1 in β†’ 1 out8.7500 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.

6.394 Γ— 10⁹⁸(99-digit number)
63945860335836549743…31877107952991974460
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
6.394 Γ— 10⁹⁸(99-digit number)
63945860335836549743…31877107952991974459
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.394 Γ— 10⁹⁸(99-digit number)
63945860335836549743…31877107952991974461
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
1.278 Γ— 10⁹⁹(100-digit number)
12789172067167309948…63754215905983948919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.278 Γ— 10⁹⁹(100-digit number)
12789172067167309948…63754215905983948921
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
2.557 Γ— 10⁹⁹(100-digit number)
25578344134334619897…27508431811967897839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.557 Γ— 10⁹⁹(100-digit number)
25578344134334619897…27508431811967897841
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
5.115 Γ— 10⁹⁹(100-digit number)
51156688268669239794…55016863623935795679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.115 Γ— 10⁹⁹(100-digit number)
51156688268669239794…55016863623935795681
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
1.023 Γ— 10¹⁰⁰(101-digit number)
10231337653733847958…10033727247871591359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.023 Γ— 10¹⁰⁰(101-digit number)
10231337653733847958…10033727247871591361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
2.046 Γ— 10¹⁰⁰(101-digit number)
20462675307467695917…20067454495743182719
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 491443

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 92b612ef5e4d8da5c36fdb96033b407032c5eb2546f87897b433b0a35e3ee5b2

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 #491,443 on Chainz β†—
Circulating Supply:57,853,277 XPMΒ·at block #6,826,143 Β· updates every 60s
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