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Block #2,636,612

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/29/2018, 3:52:56 PM Β· Difficulty 11.3909 Β· 4,197,150 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
17a13d0a530cb51058ff5afa61080beaca3eee393827b04425d203b4efe93a65
View on Chainz β†—

Difficulty

11.390933

Transactions

1

Size

201 B

Version

2

Bits

0b64142d

Nonce

1,270,960,686

Timestamp

4/29/2018, 3:52:56 PM

Confirmations

4,197,150

Merkle Root

cc1e3efc61760b40e00f5ad112a5cc24b334dbbc276cf3e0044ee6147729ec41
Transactions (1)
Coinbasecc1e3efc61760b…4ee6147729ec41
1 in β†’ 1 out7.6900 XPM110 B
ASBcMF8d…uXvHkfiw
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.

2.696 Γ— 10⁹⁷(98-digit number)
26966534115757458457…07410538220300697600
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
2.696 Γ— 10⁹⁷(98-digit number)
26966534115757458457…07410538220300697599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.696 Γ— 10⁹⁷(98-digit number)
26966534115757458457…07410538220300697601
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
5.393 Γ— 10⁹⁷(98-digit number)
53933068231514916914…14821076440601395199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.393 Γ— 10⁹⁷(98-digit number)
53933068231514916914…14821076440601395201
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
1.078 Γ— 10⁹⁸(99-digit number)
10786613646302983382…29642152881202790399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.078 Γ— 10⁹⁸(99-digit number)
10786613646302983382…29642152881202790401
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
2.157 Γ— 10⁹⁸(99-digit number)
21573227292605966765…59284305762405580799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.157 Γ— 10⁹⁸(99-digit number)
21573227292605966765…59284305762405580801
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
4.314 Γ— 10⁹⁸(99-digit number)
43146454585211933531…18568611524811161599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.314 Γ— 10⁹⁸(99-digit number)
43146454585211933531…18568611524811161601
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
8.629 Γ— 10⁹⁸(99-digit number)
86292909170423867063…37137223049622323199
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 2636612

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 17a13d0a530cb51058ff5afa61080beaca3eee393827b04425d203b4efe93a65

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 #2,636,612 on Chainz β†—
Circulating Supply:57,914,312 XPMΒ·at block #6,833,761 Β· updates every 60s
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