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Home/Chain Registry/Block #2,786,861

Block #2,786,861

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/9/2018, 9:03:16 PM Β· Difficulty 11.6730 Β· 4,053,673 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c392eaa5396c5027cf1bfb4487e214b6f2b9f5d67a12a958496c22e392933081
View on Chainz β†—

Difficulty

11.673047

Transactions

2

Size

544 B

Version

2

Bits

0bac4cd4

Nonce

432,983,955

Timestamp

8/9/2018, 9:03:16 PM

Confirmations

4,053,673

Merkle Root

4c5099e3744356d04c57a24a47e908835f7c35b847135d9900e8953055530624
Transactions (2)
Coinbasef233591c2c16ff…89d735f3b7097c
1 in β†’ 1 out7.3400 XPM110 B
AaHHg8MM…GEaxA6zw
aea28afb6a6eec…8e4618f0bb7c1d
2 in β†’ 2 out8.0300 XPM342 B
AHkw1rwv…C2xvb82dARezZb4y…FxP7ivbi
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.

2.128 Γ— 10⁹⁸(99-digit number)
21286891522313389394…70823879502838005760
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
2.128 Γ— 10⁹⁸(99-digit number)
21286891522313389394…70823879502838005759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.128 Γ— 10⁹⁸(99-digit number)
21286891522313389394…70823879502838005761
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
4.257 Γ— 10⁹⁸(99-digit number)
42573783044626778788…41647759005676011519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.257 Γ— 10⁹⁸(99-digit number)
42573783044626778788…41647759005676011521
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
8.514 Γ— 10⁹⁸(99-digit number)
85147566089253557577…83295518011352023039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.514 Γ— 10⁹⁸(99-digit number)
85147566089253557577…83295518011352023041
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
1.702 Γ— 10⁹⁹(100-digit number)
17029513217850711515…66591036022704046079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.702 Γ— 10⁹⁹(100-digit number)
17029513217850711515…66591036022704046081
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
3.405 Γ— 10⁹⁹(100-digit number)
34059026435701423031…33182072045408092159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.405 Γ— 10⁹⁹(100-digit number)
34059026435701423031…33182072045408092161
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
6.811 Γ— 10⁹⁹(100-digit number)
68118052871402846062…66364144090816184319
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 2786861

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 c392eaa5396c5027cf1bfb4487e214b6f2b9f5d67a12a958496c22e392933081

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 #2,786,861 on Chainz β†—
Circulating Supply:57,968,603 XPMΒ·at block #6,840,533 Β· updates every 60s
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