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Home/Chain Registry/Block #2,650,601

Block #2,650,601

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/6/2018, 4:26:17 AM Β· Difficulty 11.7556 Β· 4,181,405 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f2129edc58fff0ad1e61bee60716f1e70067078304f987827d86e2a09f62d0dd
View on Chainz β†—

Difficulty

11.755631

Transactions

1

Size

201 B

Version

2

Bits

0bc1710c

Nonce

622,893,591

Timestamp

5/6/2018, 4:26:17 AM

Confirmations

4,181,405

Merkle Root

f73c103e6d1aa8e1d0d82bb34d4af14ed34e5aa5962958053aa2f975e08e59b1
Transactions (1)
Coinbasef73c103e6d1aa8…a2f975e08e59b1
1 in β†’ 1 out7.2200 XPM110 B
AL7Ukq6X…uT2jh7Kj
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.

7.221 Γ— 10⁹⁢(97-digit number)
72219021364058047889…47218168570141173760
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
7.221 Γ— 10⁹⁢(97-digit number)
72219021364058047889…47218168570141173759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.221 Γ— 10⁹⁢(97-digit number)
72219021364058047889…47218168570141173761
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
1.444 Γ— 10⁹⁷(98-digit number)
14443804272811609577…94436337140282347519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.444 Γ— 10⁹⁷(98-digit number)
14443804272811609577…94436337140282347521
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
2.888 Γ— 10⁹⁷(98-digit number)
28887608545623219155…88872674280564695039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.888 Γ— 10⁹⁷(98-digit number)
28887608545623219155…88872674280564695041
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
5.777 Γ— 10⁹⁷(98-digit number)
57775217091246438311…77745348561129390079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.777 Γ— 10⁹⁷(98-digit number)
57775217091246438311…77745348561129390081
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
1.155 Γ— 10⁹⁸(99-digit number)
11555043418249287662…55490697122258780159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.155 Γ— 10⁹⁸(99-digit number)
11555043418249287662…55490697122258780161
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
2.311 Γ— 10⁹⁸(99-digit number)
23110086836498575324…10981394244517560319
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 2650601

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 f2129edc58fff0ad1e61bee60716f1e70067078304f987827d86e2a09f62d0dd

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 #2,650,601 on Chainz β†—
Circulating Supply:57,900,176 XPMΒ·at block #6,832,005 Β· updates every 60s
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