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Block #2,690,910

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/4/2018, 1:37:22 AM Β· Difficulty 11.6863 Β· 4,152,149 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
06b0106d4b2027ab79749072338a31ec99a2265d2ecab88f130c4b06f072f3fe
View on Chainz β†—

Difficulty

11.686269

Transactions

2

Size

427 B

Version

2

Bits

0bafaf4f

Nonce

76,706,843

Timestamp

6/4/2018, 1:37:22 AM

Confirmations

4,152,149

Merkle Root

6c1956e729b6c95cb21a006cf5796474b96b7f9c2688808be6af5813a3b41c21
Transactions (2)
Coinbase8a8836a2040655…1d1d6b35ddd81e
1 in β†’ 1 out7.3200 XPM110 B
AYZc7nG8…48wnBCbC
ed07320d585da2…b97d02489cb986
1 in β†’ 2 out5.2952 XPM227 B
Ad2CEpk5…v4B2KXgQAUeM8UiC…hXgyiAn1
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.

5.000 Γ— 10⁹⁴(95-digit number)
50007239676380770723…14957697306325737000
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
5.000 Γ— 10⁹⁴(95-digit number)
50007239676380770723…14957697306325736999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.000 Γ— 10⁹⁴(95-digit number)
50007239676380770723…14957697306325737001
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
1.000 Γ— 10⁹⁡(96-digit number)
10001447935276154144…29915394612651473999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.000 Γ— 10⁹⁡(96-digit number)
10001447935276154144…29915394612651474001
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
2.000 Γ— 10⁹⁡(96-digit number)
20002895870552308289…59830789225302947999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.000 Γ— 10⁹⁡(96-digit number)
20002895870552308289…59830789225302948001
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
4.000 Γ— 10⁹⁡(96-digit number)
40005791741104616579…19661578450605895999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.000 Γ— 10⁹⁡(96-digit number)
40005791741104616579…19661578450605896001
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
8.001 Γ— 10⁹⁡(96-digit number)
80011583482209233158…39323156901211791999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.001 Γ— 10⁹⁡(96-digit number)
80011583482209233158…39323156901211792001
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
1.600 Γ— 10⁹⁢(97-digit number)
16002316696441846631…78646313802423583999
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 2690910

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 06b0106d4b2027ab79749072338a31ec99a2265d2ecab88f130c4b06f072f3fe

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 #2,690,910 on Chainz β†—
Circulating Supply:57,988,831 XPMΒ·at block #6,843,058 Β· updates every 60s
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