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Home/Chain Registry/Block #2,887,229

Block #2,887,229

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/19/2018, 3:15:57 AM Β· Difficulty 11.6207 Β· 3,957,487 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
05b59deef7c66893b487751534206bbb3d66d42f8a6cfe3e1f2abb79dd5d7cd2
View on Chainz β†—

Difficulty

11.620718

Transactions

1

Size

200 B

Version

2

Bits

0b9ee763

Nonce

138,391,367

Timestamp

10/19/2018, 3:15:57 AM

Confirmations

3,957,487

Merkle Root

ffcc47325a98c3348958e75c873a6ed12b07e6bc3232b812597edc1c66ebf4d2
Transactions (1)
Coinbaseffcc47325a98c3…7edc1c66ebf4d2
1 in β†’ 1 out7.3900 XPM110 B
AUMQRepm…tAfKmdW1
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.

5.060 Γ— 10⁹³(94-digit number)
50603942273735671881…83402308591722566480
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
5.060 Γ— 10⁹³(94-digit number)
50603942273735671881…83402308591722566479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.060 Γ— 10⁹³(94-digit number)
50603942273735671881…83402308591722566481
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
1.012 Γ— 10⁹⁴(95-digit number)
10120788454747134376…66804617183445132959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.012 Γ— 10⁹⁴(95-digit number)
10120788454747134376…66804617183445132961
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
2.024 Γ— 10⁹⁴(95-digit number)
20241576909494268752…33609234366890265919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.024 Γ— 10⁹⁴(95-digit number)
20241576909494268752…33609234366890265921
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
4.048 Γ— 10⁹⁴(95-digit number)
40483153818988537505…67218468733780531839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.048 Γ— 10⁹⁴(95-digit number)
40483153818988537505…67218468733780531841
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
8.096 Γ— 10⁹⁴(95-digit number)
80966307637977075011…34436937467561063679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.096 Γ— 10⁹⁴(95-digit number)
80966307637977075011…34436937467561063681
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
1.619 Γ— 10⁹⁡(96-digit number)
16193261527595415002…68873874935122127359
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 2887229

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 05b59deef7c66893b487751534206bbb3d66d42f8a6cfe3e1f2abb79dd5d7cd2

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 #2,887,229 on Chainz β†—
Circulating Supply:58,002,137 XPMΒ·at block #6,844,715 Β· updates every 60s
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