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Home/Chain Registry/Block #2,772,892

Block #2,772,892

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/31/2018, 6:42:13 AM Β· Difficulty 11.6629 Β· 4,070,524 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
49aec598ddbf9609d0735d3118bbb9c2b21ef98bf638f312030a32027e3bc87d
View on Chainz β†—

Difficulty

11.662914

Transactions

2

Size

2.01 KB

Version

2

Bits

0ba9b4b5

Nonce

542,925,802

Timestamp

7/31/2018, 6:42:13 AM

Confirmations

4,070,524

Merkle Root

08841311de68b2179ac0b0a8358f618c7f43b8e83b5c29f16df4a373335b2f57
Transactions (2)
Coinbase74c20420921c87…76e656ebf1bfd5
1 in β†’ 1 out7.3600 XPM110 B
AceKKUY5…QfG46EQK
66478436b702f7…5a6738b23e56a5
12 in β†’ 2 out8425.6558 XPM1.81 KB
ARpj2tTQ…7UxuVfkNATGPBLmo…CFXDY7bV
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.

2.365 Γ— 10⁹⁷(98-digit number)
23652346729670212169…65188145338062991360
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
2.365 Γ— 10⁹⁷(98-digit number)
23652346729670212169…65188145338062991359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.365 Γ— 10⁹⁷(98-digit number)
23652346729670212169…65188145338062991361
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
4.730 Γ— 10⁹⁷(98-digit number)
47304693459340424338…30376290676125982719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.730 Γ— 10⁹⁷(98-digit number)
47304693459340424338…30376290676125982721
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
9.460 Γ— 10⁹⁷(98-digit number)
94609386918680848676…60752581352251965439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.460 Γ— 10⁹⁷(98-digit number)
94609386918680848676…60752581352251965441
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
1.892 Γ— 10⁹⁸(99-digit number)
18921877383736169735…21505162704503930879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.892 Γ— 10⁹⁸(99-digit number)
18921877383736169735…21505162704503930881
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
3.784 Γ— 10⁹⁸(99-digit number)
37843754767472339470…43010325409007861759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.784 Γ— 10⁹⁸(99-digit number)
37843754767472339470…43010325409007861761
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
7.568 Γ— 10⁹⁸(99-digit number)
75687509534944678941…86020650818015723519
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 2772892

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 49aec598ddbf9609d0735d3118bbb9c2b21ef98bf638f312030a32027e3bc87d

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 #2,772,892 on Chainz β†—
Circulating Supply:57,991,695 XPMΒ·at block #6,843,415 Β· updates every 60s
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