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Home/Chain Registry/Block #2,694,384

Block #2,694,384

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/6/2018, 1:54:37 PM Β· Difficulty 11.6773 Β· 4,150,512 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a701cf290e66522ab0aced6e2e1e6c233509154d2adc3a15056a8cfcdd0c764f
View on Chainz β†—

Difficulty

11.677290

Transactions

1

Size

201 B

Version

2

Bits

0bad62e6

Nonce

1,730,828,063

Timestamp

6/6/2018, 1:54:37 PM

Confirmations

4,150,512

Merkle Root

c301fe0dc3252140f9f05c13f19d51f6dbbd5493cca1f49f70e5f15ad7f5f654
Transactions (1)
Coinbasec301fe0dc32521…e5f15ad7f5f654
1 in β†’ 1 out7.3200 XPM110 B
AbSaoxLA…Dh6BHm4w
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.

1.377 Γ— 10⁹⁷(98-digit number)
13775924868995785114…80194460315854274560
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
1.377 Γ— 10⁹⁷(98-digit number)
13775924868995785114…80194460315854274559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.377 Γ— 10⁹⁷(98-digit number)
13775924868995785114…80194460315854274561
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
2.755 Γ— 10⁹⁷(98-digit number)
27551849737991570228…60388920631708549119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.755 Γ— 10⁹⁷(98-digit number)
27551849737991570228…60388920631708549121
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
5.510 Γ— 10⁹⁷(98-digit number)
55103699475983140456…20777841263417098239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.510 Γ— 10⁹⁷(98-digit number)
55103699475983140456…20777841263417098241
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
1.102 Γ— 10⁹⁸(99-digit number)
11020739895196628091…41555682526834196479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.102 Γ— 10⁹⁸(99-digit number)
11020739895196628091…41555682526834196481
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
2.204 Γ— 10⁹⁸(99-digit number)
22041479790393256182…83111365053668392959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.204 Γ— 10⁹⁸(99-digit number)
22041479790393256182…83111365053668392961
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
4.408 Γ— 10⁹⁸(99-digit number)
44082959580786512365…66222730107336785919
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 2694384

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 a701cf290e66522ab0aced6e2e1e6c233509154d2adc3a15056a8cfcdd0c764f

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 #2,694,384 on Chainz β†—
Circulating Supply:58,003,584 XPMΒ·at block #6,844,895 Β· updates every 60s
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