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Block #2,660,465

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/14/2018, 10:36:57 AM Β· Difficulty 11.6353 Β· 4,181,704 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b32adc3973c19f650914554ed46301d300eb090cd45819b2ab2311a6b7a739d2
View on Chainz β†—

Difficulty

11.635282

Transactions

1

Size

202 B

Version

2

Bits

0ba2a1d3

Nonce

671,850,588

Timestamp

5/14/2018, 10:36:57 AM

Confirmations

4,181,704

Merkle Root

c1788aba767351cdedbd8fc31073d7a044c876e707cd73d4402881fb327c6331
Transactions (1)
Coinbasec1788aba767351…2881fb327c6331
1 in β†’ 1 out7.3700 XPM110 B
ANTEPSbg…ps8SQUCL
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.

4.570 Γ— 10⁹⁹(100-digit number)
45705035865168239886…34671998988069109760
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
4.570 Γ— 10⁹⁹(100-digit number)
45705035865168239886…34671998988069109759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.570 Γ— 10⁹⁹(100-digit number)
45705035865168239886…34671998988069109761
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
9.141 Γ— 10⁹⁹(100-digit number)
91410071730336479772…69343997976138219519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.141 Γ— 10⁹⁹(100-digit number)
91410071730336479772…69343997976138219521
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
1.828 Γ— 10¹⁰⁰(101-digit number)
18282014346067295954…38687995952276439039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.828 Γ— 10¹⁰⁰(101-digit number)
18282014346067295954…38687995952276439041
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
3.656 Γ— 10¹⁰⁰(101-digit number)
36564028692134591908…77375991904552878079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.656 Γ— 10¹⁰⁰(101-digit number)
36564028692134591908…77375991904552878081
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
7.312 Γ— 10¹⁰⁰(101-digit number)
73128057384269183817…54751983809105756159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.312 Γ— 10¹⁰⁰(101-digit number)
73128057384269183817…54751983809105756161
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
1.462 Γ— 10¹⁰¹(102-digit number)
14625611476853836763…09503967618211512319
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 2660465

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 b32adc3973c19f650914554ed46301d300eb090cd45819b2ab2311a6b7a739d2

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 #2,660,465 on Chainz β†—
Circulating Supply:57,981,744 XPMΒ·at block #6,842,168 Β· updates every 60s
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