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Block #604,269

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/27/2014, 4:35:39 PM Β· Difficulty 10.9104 Β· 6,196,311 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
443017d8a05cde8fdb59b4ff570b8e1b2359d4a913241e85dc3b56d820e2bd6a
View on Chainz β†—

Height

#604,269

Difficulty

10.910388

Transactions

1

Size

200 B

Version

2

Bits

0ae90f35

Nonce

376,173,525

Timestamp

6/27/2014, 4:35:39 PM

Confirmations

6,196,311

Merkle Root

8753e6c2c6e676b5b695f888473f65ac28b7c2b0ce020a8b49997c6fcaf2c448
Transactions (1)
Coinbase8753e6c2c6e676…997c6fcaf2c448
1 in β†’ 1 out8.3900 XPM109 B
AGGNt2GX…Yjm5F6Qb
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.

1.139 Γ— 10⁹⁷(98-digit number)
11394231860015741063…16628882813369433120
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
1.139 Γ— 10⁹⁷(98-digit number)
11394231860015741063…16628882813369433119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.139 Γ— 10⁹⁷(98-digit number)
11394231860015741063…16628882813369433121
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
2.278 Γ— 10⁹⁷(98-digit number)
22788463720031482126…33257765626738866239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.278 Γ— 10⁹⁷(98-digit number)
22788463720031482126…33257765626738866241
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
4.557 Γ— 10⁹⁷(98-digit number)
45576927440062964252…66515531253477732479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.557 Γ— 10⁹⁷(98-digit number)
45576927440062964252…66515531253477732481
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
9.115 Γ— 10⁹⁷(98-digit number)
91153854880125928504…33031062506955464959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.115 Γ— 10⁹⁷(98-digit number)
91153854880125928504…33031062506955464961
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
1.823 Γ— 10⁹⁸(99-digit number)
18230770976025185700…66062125013910929919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.823 Γ— 10⁹⁸(99-digit number)
18230770976025185700…66062125013910929921
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
3.646 Γ— 10⁹⁸(99-digit number)
36461541952050371401…32124250027821859839
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 604269

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 443017d8a05cde8fdb59b4ff570b8e1b2359d4a913241e85dc3b56d820e2bd6a

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 #604,269 on Chainz β†—
Circulating Supply:57,648,697 XPMΒ·at block #6,800,579 Β· updates every 60s
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