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Home/Chain Registry/Block #2,649,816

Block #2,649,816

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/5/2018, 1:03:18 PM Β· Difficulty 11.7622 Β· 4,182,971 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7a3c1108d2536f0b2aba573fba2369badd0da03829211192cdb3663e50546a53
View on Chainz β†—

Difficulty

11.762178

Transactions

1

Size

200 B

Version

2

Bits

0bc31e12

Nonce

1,226,955,454

Timestamp

5/5/2018, 1:03:18 PM

Confirmations

4,182,971

Merkle Root

118e3fce512e47cdb50a7bcefa6973a8f385754d2a3dc3386703fc5df77d12d4
Transactions (1)
Coinbase118e3fce512e47…03fc5df77d12d4
1 in β†’ 1 out7.2200 XPM110 B
ARwzLew2…7kFLMT9B
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.

2.179 Γ— 10⁹⁡(96-digit number)
21795762093029085713…79121688503162122240
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
2.179 Γ— 10⁹⁡(96-digit number)
21795762093029085713…79121688503162122239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.179 Γ— 10⁹⁡(96-digit number)
21795762093029085713…79121688503162122241
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
4.359 Γ— 10⁹⁡(96-digit number)
43591524186058171426…58243377006324244479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.359 Γ— 10⁹⁡(96-digit number)
43591524186058171426…58243377006324244481
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
8.718 Γ— 10⁹⁡(96-digit number)
87183048372116342853…16486754012648488959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.718 Γ— 10⁹⁡(96-digit number)
87183048372116342853…16486754012648488961
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
1.743 Γ— 10⁹⁢(97-digit number)
17436609674423268570…32973508025296977919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.743 Γ— 10⁹⁢(97-digit number)
17436609674423268570…32973508025296977921
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
3.487 Γ— 10⁹⁢(97-digit number)
34873219348846537141…65947016050593955839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.487 Γ— 10⁹⁢(97-digit number)
34873219348846537141…65947016050593955841
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
6.974 Γ— 10⁹⁢(97-digit number)
69746438697693074283…31894032101187911679
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 2649816

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 7a3c1108d2536f0b2aba573fba2369badd0da03829211192cdb3663e50546a53

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 #2,649,816 on Chainz β†—
Circulating Supply:57,906,463 XPMΒ·at block #6,832,786 Β· updates every 60s
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