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Block #249,859

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/8/2013, 4:47:36 AM Β· Difficulty 9.9675 Β· 6,564,178 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e1333376e07fb32fb1d5ef979faade3b39b58240684363807eec40d172bf2728
View on Chainz β†—

Height

#249,859

Difficulty

9.967471

Transactions

1

Size

232 B

Version

2

Bits

09f7ac36

Nonce

1,835

Timestamp

11/8/2013, 4:47:36 AM

Confirmations

6,564,178

Merkle Root

9c1988dee2caf0ab15aca3c16deb962ed4f32a73f530aafdc9881a5894a9611c
Transactions (1)
Coinbase9c1988dee2caf0…881a5894a9611c
1 in β†’ 2 out10.0500 XPM141 B
AKcbk49N…GJbKa7j1AKNbfPoc…jfkpwAyL
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.

1.725 Γ— 10⁹⁢(97-digit number)
17250034318834126855…36870664546369895680
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
1.725 Γ— 10⁹⁢(97-digit number)
17250034318834126855…36870664546369895679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.725 Γ— 10⁹⁢(97-digit number)
17250034318834126855…36870664546369895681
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
3.450 Γ— 10⁹⁢(97-digit number)
34500068637668253711…73741329092739791359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.450 Γ— 10⁹⁢(97-digit number)
34500068637668253711…73741329092739791361
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
6.900 Γ— 10⁹⁢(97-digit number)
69000137275336507423…47482658185479582719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.900 Γ— 10⁹⁢(97-digit number)
69000137275336507423…47482658185479582721
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
1.380 Γ— 10⁹⁷(98-digit number)
13800027455067301484…94965316370959165439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.380 Γ— 10⁹⁷(98-digit number)
13800027455067301484…94965316370959165441
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
2.760 Γ— 10⁹⁷(98-digit number)
27600054910134602969…89930632741918330879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.760 Γ— 10⁹⁷(98-digit number)
27600054910134602969…89930632741918330881
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 249859

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 e1333376e07fb32fb1d5ef979faade3b39b58240684363807eec40d172bf2728

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 #249,859 on Chainz β†—
Circulating Supply:57,756,371 XPMΒ·at block #6,814,036 Β· updates every 60s
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