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Block #287,225

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/1/2013, 5:51:34 AM Β· Difficulty 9.9864 Β· 6,512,002 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
35a2b46408190a13c5be51e1826bba389d7d6cb4857414438f9eb0bd97f9f23d
View on Chainz β†—

Height

#287,225

Difficulty

9.986424

Transactions

1

Size

1.11 KB

Version

2

Bits

09fc8641

Nonce

9,422

Timestamp

12/1/2013, 5:51:34 AM

Confirmations

6,512,002

Merkle Root

c42293bc00d4e86c12e90575ff7636301b66199f5bfa214badb0020d9a6f3777
Transactions (1)
Coinbasec42293bc00d4e8…b0020d9a6f3777
1 in β†’ 29 out9.9900 XPM1.02 KB
AYcLTeXR…bscgPopsAGFAJ5YL…ZEnBbk6GAWZd1qVJ…9pj9yfPaALaSmG93…4TA3uNARAd9pSzHt…cpJ3y2zz
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.

2.678 Γ— 10⁹⁴(95-digit number)
26787382307630669060…48602494428748456960
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
2.678 Γ— 10⁹⁴(95-digit number)
26787382307630669060…48602494428748456959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.678 Γ— 10⁹⁴(95-digit number)
26787382307630669060…48602494428748456961
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
5.357 Γ— 10⁹⁴(95-digit number)
53574764615261338121…97204988857496913919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.357 Γ— 10⁹⁴(95-digit number)
53574764615261338121…97204988857496913921
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
1.071 Γ— 10⁹⁡(96-digit number)
10714952923052267624…94409977714993827839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.071 Γ— 10⁹⁡(96-digit number)
10714952923052267624…94409977714993827841
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
2.142 Γ— 10⁹⁡(96-digit number)
21429905846104535248…88819955429987655679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.142 Γ— 10⁹⁡(96-digit number)
21429905846104535248…88819955429987655681
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
4.285 Γ— 10⁹⁡(96-digit number)
42859811692209070497…77639910859975311359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.285 Γ— 10⁹⁡(96-digit number)
42859811692209070497…77639910859975311361
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 287225

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 35a2b46408190a13c5be51e1826bba389d7d6cb4857414438f9eb0bd97f9f23d

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 #287,225 on Chainz β†—
Circulating Supply:57,637,858 XPMΒ·at block #6,799,226 Β· updates every 60s
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