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Home/Chain Registry/Block #2,281,869

Block #2,281,869

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/4/2017, 9:10:06 AM Β· Difficulty 10.9555 Β· 4,558,319 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3a8d4c688fd6f3af8ebb2ac4d306d3718859c8dcbf242aff3ee3fd55e6f8d931
View on Chainz β†—

Difficulty

10.955528

Transactions

1

Size

202 B

Version

2

Bits

0af49d80

Nonce

168,272,362

Timestamp

9/4/2017, 9:10:06 AM

Confirmations

4,558,319

Merkle Root

728d6749620b25297d3ce94e8be6fbdba63a72d91a4b155e021455b35f020267
Transactions (1)
Coinbase728d6749620b25…1455b35f020267
1 in β†’ 1 out8.3200 XPM110 B
AUYkDnyF…Cpq24GQ2
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.

2.582 Γ— 10⁹⁸(99-digit number)
25825568511368230977…68516015517744496640
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
2.582 Γ— 10⁹⁸(99-digit number)
25825568511368230977…68516015517744496639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.582 Γ— 10⁹⁸(99-digit number)
25825568511368230977…68516015517744496641
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
5.165 Γ— 10⁹⁸(99-digit number)
51651137022736461955…37032031035488993279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.165 Γ— 10⁹⁸(99-digit number)
51651137022736461955…37032031035488993281
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
1.033 Γ— 10⁹⁹(100-digit number)
10330227404547292391…74064062070977986559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.033 Γ— 10⁹⁹(100-digit number)
10330227404547292391…74064062070977986561
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
2.066 Γ— 10⁹⁹(100-digit number)
20660454809094584782…48128124141955973119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.066 Γ— 10⁹⁹(100-digit number)
20660454809094584782…48128124141955973121
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
4.132 Γ— 10⁹⁹(100-digit number)
41320909618189169564…96256248283911946239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.132 Γ— 10⁹⁹(100-digit number)
41320909618189169564…96256248283911946241
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
8.264 Γ— 10⁹⁹(100-digit number)
82641819236378339128…92512496567823892479
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 2281869

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 3a8d4c688fd6f3af8ebb2ac4d306d3718859c8dcbf242aff3ee3fd55e6f8d931

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 #2,281,869 on Chainz β†—
Circulating Supply:57,965,828 XPMΒ·at block #6,840,187 Β· updates every 60s
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