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Block #596,964

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/21/2014, 1:09:41 PM Β· Difficulty 10.9337 Β· 6,203,680 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fb5ea7636bfb7d9d0872886f07748f20e884e1fcbd8a5207e19ddcbdedbe5f3e
View on Chainz β†—

Height

#596,964

Difficulty

10.933748

Transactions

1

Size

243 B

Version

2

Bits

0aef0a1c

Nonce

416,084,483

Timestamp

6/21/2014, 1:09:41 PM

Confirmations

6,203,680

Merkle Root

8dce925776beb34a9d049b6fcce6c7cd6af372e48b3078cef0aa44b703a4b417
Transactions (1)
Coinbase8dce925776beb3…aa44b703a4b417
1 in β†’ 2 out8.3500 XPM152 B
ATCVLUUT…UaVeq8GMALPu3s2c…EJXLjVFh
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.

6.057 Γ— 10⁹⁷(98-digit number)
60570285012348027344…96869020151629699680
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
6.057 Γ— 10⁹⁷(98-digit number)
60570285012348027344…96869020151629699679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.057 Γ— 10⁹⁷(98-digit number)
60570285012348027344…96869020151629699681
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
1.211 Γ— 10⁹⁸(99-digit number)
12114057002469605468…93738040303259399359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.211 Γ— 10⁹⁸(99-digit number)
12114057002469605468…93738040303259399361
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
2.422 Γ— 10⁹⁸(99-digit number)
24228114004939210937…87476080606518798719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.422 Γ— 10⁹⁸(99-digit number)
24228114004939210937…87476080606518798721
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
4.845 Γ— 10⁹⁸(99-digit number)
48456228009878421875…74952161213037597439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.845 Γ— 10⁹⁸(99-digit number)
48456228009878421875…74952161213037597441
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
9.691 Γ— 10⁹⁸(99-digit number)
96912456019756843751…49904322426075194879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.691 Γ— 10⁹⁸(99-digit number)
96912456019756843751…49904322426075194881
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
1.938 Γ— 10⁹⁹(100-digit number)
19382491203951368750…99808644852150389759
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 596964

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 fb5ea7636bfb7d9d0872886f07748f20e884e1fcbd8a5207e19ddcbdedbe5f3e

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 #596,964 on Chainz β†—
Circulating Supply:57,649,219 XPMΒ·at block #6,800,643 Β· updates every 60s
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