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Block #642,006

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/21/2014, 9:50:53 AM Β· Difficulty 10.9571 Β· 6,153,818 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
06add0872d7fdf8c0e32c0382989bb2f6ef98b345dfadd6e0fe1e1e04d9fb765
View on Chainz β†—

Height

#642,006

Difficulty

10.957066

Transactions

3

Size

108.45 KB

Version

2

Bits

0af5024c

Nonce

4,171,883,114

Timestamp

7/21/2014, 9:50:53 AM

Confirmations

6,153,818

Merkle Root

522d80bcd1d382f483a325e358e94375a4b52a39c6765dc3e0f4f268df39f89c
Transactions (3)
Coinbase7947000648392d…128ffeaeca858d
1 in β†’ 1 out9.4500 XPM116 B
ANSXnLY2…Sd25TjkD
9e392a9fbe2765…3f5062db07adb4
288 in β†’ 2 out2500.0100 XPM41.70 KB
AaUAHKKY…96UvUJn4AL9Gt8XW…LK4hBBR9
0b3d7b34ae0a9e…6ada1d80493800
460 in β†’ 2 out2500.0100 XPM66.55 KB
Aaf8Dqtm…yMjXJB7RAaUAHKKY…96UvUJn4
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.

1.905 Γ— 10⁹⁷(98-digit number)
19056050500175583748…22675947016477050880
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
1.905 Γ— 10⁹⁷(98-digit number)
19056050500175583748…22675947016477050879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.905 Γ— 10⁹⁷(98-digit number)
19056050500175583748…22675947016477050881
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
3.811 Γ— 10⁹⁷(98-digit number)
38112101000351167496…45351894032954101759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.811 Γ— 10⁹⁷(98-digit number)
38112101000351167496…45351894032954101761
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
7.622 Γ— 10⁹⁷(98-digit number)
76224202000702334993…90703788065908203519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.622 Γ— 10⁹⁷(98-digit number)
76224202000702334993…90703788065908203521
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
1.524 Γ— 10⁹⁸(99-digit number)
15244840400140466998…81407576131816407039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.524 Γ— 10⁹⁸(99-digit number)
15244840400140466998…81407576131816407041
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
3.048 Γ— 10⁹⁸(99-digit number)
30489680800280933997…62815152263632814079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.048 Γ— 10⁹⁸(99-digit number)
30489680800280933997…62815152263632814081
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 642006

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 06add0872d7fdf8c0e32c0382989bb2f6ef98b345dfadd6e0fe1e1e04d9fb765

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 #642,006 on Chainz β†—
Circulating Supply:57,610,674 XPMΒ·at block #6,795,823 Β· updates every 60s
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