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Home/Chain Registry/Block #2,559,893

Block #2,559,893

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/11/2018, 6:45:35 AM Β· Difficulty 10.9919 Β· 4,284,252 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
db61f2acfc346d40e1b3ba4dd2bb22c242b7ce87436ce778e7d29334fdb451b7
View on Chainz β†—

Difficulty

10.991936

Transactions

2

Size

574 B

Version

2

Bits

0afdef87

Nonce

1,671,753,706

Timestamp

3/11/2018, 6:45:35 AM

Confirmations

4,284,252

Merkle Root

696a9adc866472bbaf4b7322e236983a8127ed3e6596dc3bbd1558309635d09e
Transactions (2)
Coinbase03932123543464…89579b69239369
1 in β†’ 1 out8.2700 XPM110 B
ARmw6b3e…JNG2Qx1P
459f778f2933d2…722a91ffbc16b4
2 in β†’ 2 out13.0300 XPM374 B
AMJrJD7z…ismhARybAHZRKKFA…ELvY2MKQ
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.

4.072 Γ— 10⁹⁴(95-digit number)
40723636093327765952…08511014400484162480
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
4.072 Γ— 10⁹⁴(95-digit number)
40723636093327765952…08511014400484162479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.072 Γ— 10⁹⁴(95-digit number)
40723636093327765952…08511014400484162481
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
8.144 Γ— 10⁹⁴(95-digit number)
81447272186655531905…17022028800968324959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.144 Γ— 10⁹⁴(95-digit number)
81447272186655531905…17022028800968324961
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
1.628 Γ— 10⁹⁡(96-digit number)
16289454437331106381…34044057601936649919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.628 Γ— 10⁹⁡(96-digit number)
16289454437331106381…34044057601936649921
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
3.257 Γ— 10⁹⁡(96-digit number)
32578908874662212762…68088115203873299839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.257 Γ— 10⁹⁡(96-digit number)
32578908874662212762…68088115203873299841
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
6.515 Γ— 10⁹⁡(96-digit number)
65157817749324425524…36176230407746599679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.515 Γ— 10⁹⁡(96-digit number)
65157817749324425524…36176230407746599681
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
1.303 Γ— 10⁹⁢(97-digit number)
13031563549864885104…72352460815493199359
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 2559893

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 db61f2acfc346d40e1b3ba4dd2bb22c242b7ce87436ce778e7d29334fdb451b7

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 #2,559,893 on Chainz β†—
Circulating Supply:57,997,536 XPMΒ·at block #6,844,144 Β· updates every 60s
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