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Home/Chain Registry/Block #3,503,306

Block #3,503,306

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/7/2020, 3:24:14 AM Β· Difficulty 10.9306 Β· 3,339,881 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4dcbfab7b7fe3aa4ef0235d5c5daa862a71d1c234bebc3b09bb366e7029915a7
View on Chainz β†—

Difficulty

10.930636

Transactions

1

Size

201 B

Version

2

Bits

0aee3e22

Nonce

69,814,755

Timestamp

1/7/2020, 3:24:14 AM

Confirmations

3,339,881

Merkle Root

3321e114bcf54771165f4c57ba5f0e07d0243c0ea5ff2a6c8c5e6d9bc418b878
Transactions (1)
Coinbase3321e114bcf547…5e6d9bc418b878
1 in β†’ 1 out8.3600 XPM110 B
ASiq2qtK…VMhmk7yL
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.

6.765 Γ— 10⁹⁷(98-digit number)
67653599976828761188…99461073075608207360
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
6.765 Γ— 10⁹⁷(98-digit number)
67653599976828761188…99461073075608207359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.765 Γ— 10⁹⁷(98-digit number)
67653599976828761188…99461073075608207361
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
1.353 Γ— 10⁹⁸(99-digit number)
13530719995365752237…98922146151216414719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.353 Γ— 10⁹⁸(99-digit number)
13530719995365752237…98922146151216414721
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
2.706 Γ— 10⁹⁸(99-digit number)
27061439990731504475…97844292302432829439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.706 Γ— 10⁹⁸(99-digit number)
27061439990731504475…97844292302432829441
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
5.412 Γ— 10⁹⁸(99-digit number)
54122879981463008950…95688584604865658879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.412 Γ— 10⁹⁸(99-digit number)
54122879981463008950…95688584604865658881
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
1.082 Γ— 10⁹⁹(100-digit number)
10824575996292601790…91377169209731317759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.082 Γ— 10⁹⁹(100-digit number)
10824575996292601790…91377169209731317761
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 3503306

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 4dcbfab7b7fe3aa4ef0235d5c5daa862a71d1c234bebc3b09bb366e7029915a7

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 #3,503,306 on Chainz β†—
Circulating Supply:57,989,864 XPMΒ·at block #6,843,186 Β· updates every 60s
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