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Home/Chain Registry/Block #2,829,525

Block #2,829,525

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/8/2018, 1:28:23 AM Β· Difficulty 11.7133 Β· 4,014,979 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6fdba70ecab0d392ac957c91a1ce35ad76e18635e5ddbfdeebe1f11768a5b016
View on Chainz β†—

Difficulty

11.713340

Transactions

2

Size

575 B

Version

2

Bits

0bb69d75

Nonce

1,865,393,472

Timestamp

9/8/2018, 1:28:23 AM

Confirmations

4,014,979

Merkle Root

787e5bdcca59f0e0571b8bc5484227671d7ad9f38e91e2a5e4c3e7b6d7c1e232
Transactions (2)
Coinbase53de7151b6ab00…7358845231e3a9
1 in β†’ 1 out7.2900 XPM110 B
AGAo1gUL…BhVyYsPQ
6840780748618e…92495fb763045a
2 in β†’ 2 out182.3022 XPM375 B
AaCt2Z2e…QB2Doko7AMWDTU6w…21BSF3qD
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.

1.488 Γ— 10⁹⁴(95-digit number)
14883665327679418184…90205225730591096320
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
1.488 Γ— 10⁹⁴(95-digit number)
14883665327679418184…90205225730591096319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.488 Γ— 10⁹⁴(95-digit number)
14883665327679418184…90205225730591096321
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
2.976 Γ— 10⁹⁴(95-digit number)
29767330655358836368…80410451461182192639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.976 Γ— 10⁹⁴(95-digit number)
29767330655358836368…80410451461182192641
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
5.953 Γ— 10⁹⁴(95-digit number)
59534661310717672737…60820902922364385279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.953 Γ— 10⁹⁴(95-digit number)
59534661310717672737…60820902922364385281
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
1.190 Γ— 10⁹⁡(96-digit number)
11906932262143534547…21641805844728770559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.190 Γ— 10⁹⁡(96-digit number)
11906932262143534547…21641805844728770561
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
2.381 Γ— 10⁹⁡(96-digit number)
23813864524287069094…43283611689457541119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.381 Γ— 10⁹⁡(96-digit number)
23813864524287069094…43283611689457541121
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
4.762 Γ— 10⁹⁡(96-digit number)
47627729048574138189…86567223378915082239
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 2829525

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 6fdba70ecab0d392ac957c91a1ce35ad76e18635e5ddbfdeebe1f11768a5b016

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 #2,829,525 on Chainz β†—
Circulating Supply:58,000,430 XPMΒ·at block #6,844,503 Β· updates every 60s
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