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Home/Chain Registry/Block #2,633,873

Block #2,633,873

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/28/2018, 3:47:06 PM Β· Difficulty 11.2126 Β· 4,208,489 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f8a8dc688740870670f7fa63d3ccdd54610926ae0a3d3372c8042065fc091dbd
View on Chainz β†—

Difficulty

11.212649

Transactions

1

Size

201 B

Version

2

Bits

0b367023

Nonce

86,876,483

Timestamp

4/28/2018, 3:47:06 PM

Confirmations

4,208,489

Merkle Root

698d3b898b866580a8efe80819c2ce4f70b4662e0f483cb5a36a6d25b891bec1
Transactions (1)
Coinbase698d3b898b8665…6a6d25b891bec1
1 in β†’ 1 out7.9400 XPM110 B
ALKGt7Y9…xmsS6Wh1
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.

2.419 Γ— 10⁹⁢(97-digit number)
24196626415952670504…57197237508911018560
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
2.419 Γ— 10⁹⁢(97-digit number)
24196626415952670504…57197237508911018559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.419 Γ— 10⁹⁢(97-digit number)
24196626415952670504…57197237508911018561
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
4.839 Γ— 10⁹⁢(97-digit number)
48393252831905341009…14394475017822037119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.839 Γ— 10⁹⁢(97-digit number)
48393252831905341009…14394475017822037121
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
9.678 Γ— 10⁹⁢(97-digit number)
96786505663810682018…28788950035644074239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.678 Γ— 10⁹⁢(97-digit number)
96786505663810682018…28788950035644074241
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
1.935 Γ— 10⁹⁷(98-digit number)
19357301132762136403…57577900071288148479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.935 Γ— 10⁹⁷(98-digit number)
19357301132762136403…57577900071288148481
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
3.871 Γ— 10⁹⁷(98-digit number)
38714602265524272807…15155800142576296959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.871 Γ— 10⁹⁷(98-digit number)
38714602265524272807…15155800142576296961
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
7.742 Γ— 10⁹⁷(98-digit number)
77429204531048545614…30311600285152593919
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 2633873

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 f8a8dc688740870670f7fa63d3ccdd54610926ae0a3d3372c8042065fc091dbd

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 #2,633,873 on Chainz β†—
Circulating Supply:57,983,304 XPMΒ·at block #6,842,361 Β· updates every 60s
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