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Block #3,233,321

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/20/2019, 12:13:23 PM Β· Difficulty 10.9961 Β· 3,607,779 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4fa0b3e9ab387dcef7874e70d427b968933106e73e53a5f1175b8fd87332f883
View on Chainz β†—

Difficulty

10.996073

Transactions

2

Size

428 B

Version

2

Bits

0afefeac

Nonce

127,297,246

Timestamp

6/20/2019, 12:13:23 PM

Confirmations

3,607,779

Merkle Root

70d053200951f4a8ff3212ac3d8b8fad22e03311777bcc65c791a30d0987224a
Transactions (2)
Coinbase3f26f3f38dcfc6…fe19aaf0229151
1 in β†’ 1 out8.2700 XPM110 B
AbXwmGxD…4XXYP765
c8c3661aa7b58c…f10d4aa3f21014
1 in β†’ 2 out6.2141 XPM227 B
AbXwmGxD…4XXYP765AefCLvk5…Z2a6ttS2
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.

4.038 Γ— 10⁹⁷(98-digit number)
40386447996475070114…88191266458158858240
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
4.038 Γ— 10⁹⁷(98-digit number)
40386447996475070114…88191266458158858239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.038 Γ— 10⁹⁷(98-digit number)
40386447996475070114…88191266458158858241
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
8.077 Γ— 10⁹⁷(98-digit number)
80772895992950140229…76382532916317716479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.077 Γ— 10⁹⁷(98-digit number)
80772895992950140229…76382532916317716481
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
1.615 Γ— 10⁹⁸(99-digit number)
16154579198590028045…52765065832635432959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.615 Γ— 10⁹⁸(99-digit number)
16154579198590028045…52765065832635432961
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
3.230 Γ— 10⁹⁸(99-digit number)
32309158397180056091…05530131665270865919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.230 Γ— 10⁹⁸(99-digit number)
32309158397180056091…05530131665270865921
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
6.461 Γ— 10⁹⁸(99-digit number)
64618316794360112183…11060263330541731839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.461 Γ— 10⁹⁸(99-digit number)
64618316794360112183…11060263330541731841
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
1.292 Γ— 10⁹⁹(100-digit number)
12923663358872022436…22120526661083463679
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 3233321

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 4fa0b3e9ab387dcef7874e70d427b968933106e73e53a5f1175b8fd87332f883

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 #3,233,321 on Chainz β†—
Circulating Supply:57,973,166 XPMΒ·at block #6,841,099 Β· updates every 60s
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