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Home/Chain Registry/Block #2,793,087

Block #2,793,087

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/14/2018, 3:24:20 AM Β· Difficulty 11.6788 Β· 4,050,050 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8c3d4e54ed4b8db5abdda442b70a46cd9159776858c58df72d3fd05022226844
View on Chainz β†—

Difficulty

11.678762

Transactions

1

Size

199 B

Version

2

Bits

0badc35e

Nonce

1,220,418,476

Timestamp

8/14/2018, 3:24:20 AM

Confirmations

4,050,050

Merkle Root

3009266141a6cabbb27764d04cf4bb4c9b8d6b539fe859e12cbcf22fbd769a93
Transactions (1)
Coinbase3009266141a6ca…bcf22fbd769a93
1 in β†’ 1 out7.3200 XPM110 B
AMqnSQiA…XWAjboKt
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.

3.967 Γ— 10⁹²(93-digit number)
39676936325383616833…90076970011818860080
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
3.967 Γ— 10⁹²(93-digit number)
39676936325383616833…90076970011818860079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.967 Γ— 10⁹²(93-digit number)
39676936325383616833…90076970011818860081
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
7.935 Γ— 10⁹²(93-digit number)
79353872650767233667…80153940023637720159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.935 Γ— 10⁹²(93-digit number)
79353872650767233667…80153940023637720161
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
1.587 Γ— 10⁹³(94-digit number)
15870774530153446733…60307880047275440319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.587 Γ— 10⁹³(94-digit number)
15870774530153446733…60307880047275440321
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
3.174 Γ— 10⁹³(94-digit number)
31741549060306893466…20615760094550880639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.174 Γ— 10⁹³(94-digit number)
31741549060306893466…20615760094550880641
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
6.348 Γ— 10⁹³(94-digit number)
63483098120613786933…41231520189101761279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.348 Γ— 10⁹³(94-digit number)
63483098120613786933…41231520189101761281
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
1.269 Γ— 10⁹⁴(95-digit number)
12696619624122757386…82463040378203522559
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 2793087

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 8c3d4e54ed4b8db5abdda442b70a46cd9159776858c58df72d3fd05022226844

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 #2,793,087 on Chainz β†—
Circulating Supply:57,989,460 XPMΒ·at block #6,843,136 Β· updates every 60s
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