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Home/Chain Registry/Block #2,773,788

Block #2,773,788

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 7/31/2018, 9:36:19 PM Β· Difficulty 11.6630 Β· 4,071,366 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0b79bc419bd261f4d7d597441abf84d2ce31f2b382681d0a123b282aa01a94ac
View on Chainz β†—

Difficulty

11.662994

Transactions

1

Size

200 B

Version

2

Bits

0ba9b9f4

Nonce

1,677,949,576

Timestamp

7/31/2018, 9:36:19 PM

Confirmations

4,071,366

Merkle Root

f2d55ad7ee61a0ddd80bfccea697e202dd2655a4240ded0e5dca85f7bfc45704
Transactions (1)
Coinbasef2d55ad7ee61a0…ca85f7bfc45704
1 in β†’ 1 out7.3400 XPM110 B
AdJTYg8V…yFrQbQXn
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.

1.347 Γ— 10⁹⁡(96-digit number)
13477151735296243504…69817587098627092480
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
1.347 Γ— 10⁹⁡(96-digit number)
13477151735296243504…69817587098627092479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.347 Γ— 10⁹⁡(96-digit number)
13477151735296243504…69817587098627092481
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
2.695 Γ— 10⁹⁡(96-digit number)
26954303470592487008…39635174197254184959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.695 Γ— 10⁹⁡(96-digit number)
26954303470592487008…39635174197254184961
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
5.390 Γ— 10⁹⁡(96-digit number)
53908606941184974016…79270348394508369919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.390 Γ— 10⁹⁡(96-digit number)
53908606941184974016…79270348394508369921
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
1.078 Γ— 10⁹⁢(97-digit number)
10781721388236994803…58540696789016739839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.078 Γ— 10⁹⁢(97-digit number)
10781721388236994803…58540696789016739841
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
2.156 Γ— 10⁹⁢(97-digit number)
21563442776473989606…17081393578033479679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.156 Γ— 10⁹⁢(97-digit number)
21563442776473989606…17081393578033479681
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
4.312 Γ— 10⁹⁢(97-digit number)
43126885552947979213…34162787156066959359
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
4.312 Γ— 10⁹⁢(97-digit number)
43126885552947979213…34162787156066959361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2773788

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 0b79bc419bd261f4d7d597441abf84d2ce31f2b382681d0a123b282aa01a94ac

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 #2,773,788 on Chainz β†—
Circulating Supply:58,005,660 XPMΒ·at block #6,845,153 Β· updates every 60s
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