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Home/Chain Registry/Block #2,815,558

Block #2,815,558

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/29/2018, 4:38:55 PM Β· Difficulty 11.6843 Β· 4,026,780 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
659935efca9aa0a4aa84db040a93e14d803676f9beb436ecbc07c19d9186e44d
View on Chainz β†—

Difficulty

11.684307

Transactions

1

Size

200 B

Version

2

Bits

0baf2ec2

Nonce

534,079,344

Timestamp

8/29/2018, 4:38:55 PM

Confirmations

4,026,780

Merkle Root

3fc9637c5e3ba6abae8057f9bee4f53331dcccff3b64de05b794bf23059e6aaa
Transactions (1)
Coinbase3fc9637c5e3ba6…94bf23059e6aaa
1 in β†’ 1 out7.3100 XPM110 B
ANjpevJg…zHnndZPz
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.

7.951 Γ— 10⁹⁴(95-digit number)
79511128099080346583…00414483860223511040
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
7.951 Γ— 10⁹⁴(95-digit number)
79511128099080346583…00414483860223511039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.951 Γ— 10⁹⁴(95-digit number)
79511128099080346583…00414483860223511041
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
1.590 Γ— 10⁹⁡(96-digit number)
15902225619816069316…00828967720447022079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.590 Γ— 10⁹⁡(96-digit number)
15902225619816069316…00828967720447022081
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
3.180 Γ— 10⁹⁡(96-digit number)
31804451239632138633…01657935440894044159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.180 Γ— 10⁹⁡(96-digit number)
31804451239632138633…01657935440894044161
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
6.360 Γ— 10⁹⁡(96-digit number)
63608902479264277267…03315870881788088319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.360 Γ— 10⁹⁡(96-digit number)
63608902479264277267…03315870881788088321
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
1.272 Γ— 10⁹⁢(97-digit number)
12721780495852855453…06631741763576176639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.272 Γ— 10⁹⁢(97-digit number)
12721780495852855453…06631741763576176641
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
2.544 Γ— 10⁹⁢(97-digit number)
25443560991705710906…13263483527152353279
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 2815558

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 659935efca9aa0a4aa84db040a93e14d803676f9beb436ecbc07c19d9186e44d

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 #2,815,558 on Chainz β†—
Circulating Supply:57,983,111 XPMΒ·at block #6,842,337 Β· updates every 60s
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