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Home/Chain Registry/Block #2,871,430

Block #2,871,430

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/7/2018, 5:16:06 PM Β· Difficulty 11.6655 Β· 3,969,095 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
077e99e06e1ed075be55e26230327282980be504e993e82dc6c2c635f124f97e
View on Chainz β†—

Difficulty

11.665481

Transactions

1

Size

200 B

Version

2

Bits

0baa5cf9

Nonce

526,111,142

Timestamp

10/7/2018, 5:16:06 PM

Confirmations

3,969,095

Merkle Root

b95df81ad7468854f47074eb6ac2f9803d565712df33d884e1f8c0cfb7582ccd
Transactions (1)
Coinbaseb95df81ad74688…f8c0cfb7582ccd
1 in β†’ 1 out7.3400 XPM110 B
AFpyeJpb…fuBHx7BD
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.

3.547 Γ— 10⁹⁴(95-digit number)
35471876182678419078…32745996733774195200
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
3.547 Γ— 10⁹⁴(95-digit number)
35471876182678419078…32745996733774195199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.547 Γ— 10⁹⁴(95-digit number)
35471876182678419078…32745996733774195201
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
7.094 Γ— 10⁹⁴(95-digit number)
70943752365356838157…65491993467548390399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.094 Γ— 10⁹⁴(95-digit number)
70943752365356838157…65491993467548390401
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
1.418 Γ— 10⁹⁡(96-digit number)
14188750473071367631…30983986935096780799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.418 Γ— 10⁹⁡(96-digit number)
14188750473071367631…30983986935096780801
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
2.837 Γ— 10⁹⁡(96-digit number)
28377500946142735263…61967973870193561599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.837 Γ— 10⁹⁡(96-digit number)
28377500946142735263…61967973870193561601
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
5.675 Γ— 10⁹⁡(96-digit number)
56755001892285470526…23935947740387123199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.675 Γ— 10⁹⁡(96-digit number)
56755001892285470526…23935947740387123201
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
1.135 Γ— 10⁹⁢(97-digit number)
11351000378457094105…47871895480774246399
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 2871430

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 077e99e06e1ed075be55e26230327282980be504e993e82dc6c2c635f124f97e

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 #2,871,430 on Chainz β†—
Circulating Supply:57,968,529 XPMΒ·at block #6,840,524 Β· updates every 60s
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