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Block #208,577

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/14/2013, 2:06:39 AM Β· Difficulty 9.9070 Β· 6,591,690 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
19be35978ff68f5f7d633fa942e7f492423d98656cf5021868dce0910fb74f6c
View on Chainz β†—

Height

#208,577

Difficulty

9.907013

Transactions

1

Size

200 B

Version

2

Bits

09e831f9

Nonce

7,370

Timestamp

10/14/2013, 2:06:39 AM

Confirmations

6,591,690

Merkle Root

d212ddb7672a1cf3b602bac752b74418d564de8ea715b114d0c1b01d3261ecfd
Transactions (1)
Coinbased212ddb7672a1c…c1b01d3261ecfd
1 in β†’ 1 out10.1700 XPM110 B
AbuU1HhS…JPwsJEbB
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.

4.263 Γ— 10⁹⁴(95-digit number)
42630414036664625075…14601070501419774080
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
4.263 Γ— 10⁹⁴(95-digit number)
42630414036664625075…14601070501419774079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.263 Γ— 10⁹⁴(95-digit number)
42630414036664625075…14601070501419774081
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
8.526 Γ— 10⁹⁴(95-digit number)
85260828073329250150…29202141002839548159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.526 Γ— 10⁹⁴(95-digit number)
85260828073329250150…29202141002839548161
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
1.705 Γ— 10⁹⁡(96-digit number)
17052165614665850030…58404282005679096319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.705 Γ— 10⁹⁡(96-digit number)
17052165614665850030…58404282005679096321
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
3.410 Γ— 10⁹⁡(96-digit number)
34104331229331700060…16808564011358192639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.410 Γ— 10⁹⁡(96-digit number)
34104331229331700060…16808564011358192641
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
6.820 Γ— 10⁹⁡(96-digit number)
68208662458663400120…33617128022716385279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.820 Γ— 10⁹⁡(96-digit number)
68208662458663400120…33617128022716385281
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 208577

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 19be35978ff68f5f7d633fa942e7f492423d98656cf5021868dce0910fb74f6c

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 #208,577 on Chainz β†—
Circulating Supply:57,646,193 XPMΒ·at block #6,800,266 Β· updates every 60s
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