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Home/Chain Registry/Block #2,651,882

Block #2,651,882

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/7/2018, 4:21:58 AM Β· Difficulty 11.7480 Β· 4,185,067 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0d1895a9c89a17b2d42055c92701647e53c19ae7522274053ffe075e5558b47f
View on Chainz β†—

Difficulty

11.748047

Transactions

1

Size

199 B

Version

2

Bits

0bbf8009

Nonce

703,238,764

Timestamp

5/7/2018, 4:21:58 AM

Confirmations

4,185,067

Merkle Root

a7e529230085c52572a0b0c3fa91f6c4ceeaa9584ec84ce92846b4d115f59703
Transactions (1)
Coinbasea7e529230085c5…46b4d115f59703
1 in β†’ 1 out7.2300 XPM109 B
AGGtJpsn…1BYU5A8D
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.

1.227 Γ— 10⁹⁡(96-digit number)
12279494145600692320…07417433517250633170
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
1.227 Γ— 10⁹⁡(96-digit number)
12279494145600692320…07417433517250633169
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.227 Γ— 10⁹⁡(96-digit number)
12279494145600692320…07417433517250633171
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
2.455 Γ— 10⁹⁡(96-digit number)
24558988291201384641…14834867034501266339
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.455 Γ— 10⁹⁡(96-digit number)
24558988291201384641…14834867034501266341
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
4.911 Γ— 10⁹⁡(96-digit number)
49117976582402769283…29669734069002532679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.911 Γ— 10⁹⁡(96-digit number)
49117976582402769283…29669734069002532681
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
9.823 Γ— 10⁹⁡(96-digit number)
98235953164805538567…59339468138005065359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.823 Γ— 10⁹⁡(96-digit number)
98235953164805538567…59339468138005065361
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
1.964 Γ— 10⁹⁢(97-digit number)
19647190632961107713…18678936276010130719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.964 Γ— 10⁹⁢(97-digit number)
19647190632961107713…18678936276010130721
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
3.929 Γ— 10⁹⁢(97-digit number)
39294381265922215427…37357872552020261439
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 2651882

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 0d1895a9c89a17b2d42055c92701647e53c19ae7522274053ffe075e5558b47f

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 #2,651,882 on Chainz β†—
Circulating Supply:57,939,891 XPMΒ·at block #6,836,948 Β· updates every 60s
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