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Home/Chain Registry/Block #2,647,362

Block #2,647,362

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/3/2018, 9:29:45 PM Β· Difficulty 11.7583 Β· 4,190,771 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
99dc743ce5e3e851980035d0082e0d344a0658071ef5525439aec601bb47c662
View on Chainz β†—

Difficulty

11.758295

Transactions

2

Size

1.08 KB

Version

2

Bits

0bc21f97

Nonce

4,170,436

Timestamp

5/3/2018, 9:29:45 PM

Confirmations

4,190,771

Merkle Root

1b6658eb265d83c24cfe776f1e067d64e41512c2bcad626747c301217c580547
Transactions (2)
Coinbase2d24247979aa77…22c0c663581048
1 in β†’ 1 out7.2300 XPM110 B
Adqah8zh…1WwoHJ9t
854847a28e410a…943523dd48eeda
7 in β†’ 2 out51.6851 XPM906 B
AN5byFeZ…yMp87Kb4AWp4iAg7…FUBLEm8x
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.

4.176 Γ— 10⁹⁢(97-digit number)
41765637422907450637…31257575259633745920
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
4.176 Γ— 10⁹⁢(97-digit number)
41765637422907450637…31257575259633745919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.176 Γ— 10⁹⁢(97-digit number)
41765637422907450637…31257575259633745921
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
8.353 Γ— 10⁹⁢(97-digit number)
83531274845814901275…62515150519267491839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.353 Γ— 10⁹⁢(97-digit number)
83531274845814901275…62515150519267491841
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
1.670 Γ— 10⁹⁷(98-digit number)
16706254969162980255…25030301038534983679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.670 Γ— 10⁹⁷(98-digit number)
16706254969162980255…25030301038534983681
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
3.341 Γ— 10⁹⁷(98-digit number)
33412509938325960510…50060602077069967359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.341 Γ— 10⁹⁷(98-digit number)
33412509938325960510…50060602077069967361
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
6.682 Γ— 10⁹⁷(98-digit number)
66825019876651921020…00121204154139934719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.682 Γ— 10⁹⁷(98-digit number)
66825019876651921020…00121204154139934721
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
1.336 Γ— 10⁹⁸(99-digit number)
13365003975330384204…00242408308279869439
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 2647362

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 99dc743ce5e3e851980035d0082e0d344a0658071ef5525439aec601bb47c662

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 #2,647,362 on Chainz β†—
Circulating Supply:57,949,331 XPMΒ·at block #6,838,132 Β· updates every 60s
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