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Home/Chain Registry/Block #2,813,138

Block #2,813,138

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/28/2018, 2:24:33 AM Β· Difficulty 11.6764 Β· 4,030,189 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ba3d7ad702e023e2a3d68e8db8fdaec7fc5deaa7e22b697f7f3cab35576b7da4
View on Chainz β†—

Difficulty

11.676366

Transactions

1

Size

200 B

Version

2

Bits

0bad2656

Nonce

1,517,876,909

Timestamp

8/28/2018, 2:24:33 AM

Confirmations

4,030,189

Merkle Root

c473e121112bd455259b09c62cf460d05040e968a779f27a24db5722dd138178
Transactions (1)
Coinbasec473e121112bd4…db5722dd138178
1 in β†’ 1 out7.3200 XPM110 B
AYJSUCJw…1HwKQgGQ
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.

6.892 Γ— 10⁹⁡(96-digit number)
68921641882676439556…72816180902047878400
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
6.892 Γ— 10⁹⁡(96-digit number)
68921641882676439556…72816180902047878399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.892 Γ— 10⁹⁡(96-digit number)
68921641882676439556…72816180902047878401
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
1.378 Γ— 10⁹⁢(97-digit number)
13784328376535287911…45632361804095756799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.378 Γ— 10⁹⁢(97-digit number)
13784328376535287911…45632361804095756801
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
2.756 Γ— 10⁹⁢(97-digit number)
27568656753070575822…91264723608191513599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.756 Γ— 10⁹⁢(97-digit number)
27568656753070575822…91264723608191513601
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
5.513 Γ— 10⁹⁢(97-digit number)
55137313506141151645…82529447216383027199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.513 Γ— 10⁹⁢(97-digit number)
55137313506141151645…82529447216383027201
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
1.102 Γ— 10⁹⁷(98-digit number)
11027462701228230329…65058894432766054399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.102 Γ— 10⁹⁷(98-digit number)
11027462701228230329…65058894432766054401
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
2.205 Γ— 10⁹⁷(98-digit number)
22054925402456460658…30117788865532108799
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 2813138

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 ba3d7ad702e023e2a3d68e8db8fdaec7fc5deaa7e22b697f7f3cab35576b7da4

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 #2,813,138 on Chainz β†—
Circulating Supply:57,990,977 XPMΒ·at block #6,843,326 Β· updates every 60s
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