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Home/Chain Registry/Block #2,870,633

Block #2,870,633

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/7/2018, 4:03:44 AM Β· Difficulty 11.6651 Β· 3,970,908 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
75ea131c500bf132949fdc202fa76e9554d1eaf93508369eadb0a10c5a7d38b3
View on Chainz β†—

Difficulty

11.665117

Transactions

1

Size

200 B

Version

2

Bits

0baa451e

Nonce

1,241,855,781

Timestamp

10/7/2018, 4:03:44 AM

Confirmations

3,970,908

Merkle Root

01e4ee2bed3b934d1cd6ab10297424bf1d234464e113b9161219cd27eb67bf12
Transactions (1)
Coinbase01e4ee2bed3b93…19cd27eb67bf12
1 in β†’ 1 out7.3400 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.

2.766 Γ— 10⁹⁡(96-digit number)
27665057769544035474…84969650648690798440
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
2.766 Γ— 10⁹⁡(96-digit number)
27665057769544035474…84969650648690798439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.766 Γ— 10⁹⁡(96-digit number)
27665057769544035474…84969650648690798441
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
5.533 Γ— 10⁹⁡(96-digit number)
55330115539088070949…69939301297381596879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.533 Γ— 10⁹⁡(96-digit number)
55330115539088070949…69939301297381596881
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
1.106 Γ— 10⁹⁢(97-digit number)
11066023107817614189…39878602594763193759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.106 Γ— 10⁹⁢(97-digit number)
11066023107817614189…39878602594763193761
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
2.213 Γ— 10⁹⁢(97-digit number)
22132046215635228379…79757205189526387519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.213 Γ— 10⁹⁢(97-digit number)
22132046215635228379…79757205189526387521
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
4.426 Γ— 10⁹⁢(97-digit number)
44264092431270456759…59514410379052775039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.426 Γ— 10⁹⁢(97-digit number)
44264092431270456759…59514410379052775041
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
8.852 Γ— 10⁹⁢(97-digit number)
88528184862540913518…19028820758105550079
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 2870633

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 75ea131c500bf132949fdc202fa76e9554d1eaf93508369eadb0a10c5a7d38b3

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 #2,870,633 on Chainz β†—
Circulating Supply:57,976,712 XPMΒ·at block #6,841,540 Β· updates every 60s
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