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Home/Chain Registry/Block #2,869,278

Block #2,869,278

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/6/2018, 4:08:46 AM Β· Difficulty 11.6705 Β· 3,972,513 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d90ac12cbb3cf4339aa6e9b64381dbc71e678466f82496c5259df30dc3e1eac5
View on Chainz β†—

Difficulty

11.670490

Transactions

1

Size

201 B

Version

2

Bits

0baba53f

Nonce

95,002,145

Timestamp

10/6/2018, 4:08:46 AM

Confirmations

3,972,513

Merkle Root

a4da0efa387ae879070cd71fde34e11b6e0eb2efcff90c4b367ac381d05869ae
Transactions (1)
Coinbasea4da0efa387ae8…7ac381d05869ae
1 in β†’ 1 out7.3300 XPM110 B
AQVcYBoi…CukApe9H
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.

7.654 Γ— 10⁹⁢(97-digit number)
76543130200359753253…90953824875595033600
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
7.654 Γ— 10⁹⁢(97-digit number)
76543130200359753253…90953824875595033599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.654 Γ— 10⁹⁢(97-digit number)
76543130200359753253…90953824875595033601
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
1.530 Γ— 10⁹⁷(98-digit number)
15308626040071950650…81907649751190067199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.530 Γ— 10⁹⁷(98-digit number)
15308626040071950650…81907649751190067201
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
3.061 Γ— 10⁹⁷(98-digit number)
30617252080143901301…63815299502380134399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.061 Γ— 10⁹⁷(98-digit number)
30617252080143901301…63815299502380134401
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
6.123 Γ— 10⁹⁷(98-digit number)
61234504160287802602…27630599004760268799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.123 Γ— 10⁹⁷(98-digit number)
61234504160287802602…27630599004760268801
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
1.224 Γ— 10⁹⁸(99-digit number)
12246900832057560520…55261198009520537599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.224 Γ— 10⁹⁸(99-digit number)
12246900832057560520…55261198009520537601
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
2.449 Γ— 10⁹⁸(99-digit number)
24493801664115121041…10522396019041075199
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 2869278

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 d90ac12cbb3cf4339aa6e9b64381dbc71e678466f82496c5259df30dc3e1eac5

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 #2,869,278 on Chainz β†—
Circulating Supply:57,978,706 XPMΒ·at block #6,841,790 Β· updates every 60s
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