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Block #491,321

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/14/2014, 10:48:09 AM Β· Difficulty 10.6804 Β· 6,322,510 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
25bd7e9f29ee3cc12361991b8ff2e93453dffb85639d7da888edf58af1714b1e
View on Chainz β†—

Height

#491,321

Difficulty

10.680436

Transactions

1

Size

203 B

Version

2

Bits

0aae310a

Nonce

51,963

Timestamp

4/14/2014, 10:48:09 AM

Confirmations

6,322,510

Merkle Root

3cb440f09b642a47dd7bbc579f3dacc6a79a5f310c9d91b40cc2d977e41e3724
Transactions (1)
Coinbase3cb440f09b642a…c2d977e41e3724
1 in β†’ 1 out8.7500 XPM112 B
AJeLVLy2…VBEv8Bq4
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.

1.146 Γ— 10⁹⁢(97-digit number)
11461324450211202165…86531560101405894780
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
1.146 Γ— 10⁹⁢(97-digit number)
11461324450211202165…86531560101405894779
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.146 Γ— 10⁹⁢(97-digit number)
11461324450211202165…86531560101405894781
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
2.292 Γ— 10⁹⁢(97-digit number)
22922648900422404331…73063120202811789559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.292 Γ— 10⁹⁢(97-digit number)
22922648900422404331…73063120202811789561
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
4.584 Γ— 10⁹⁢(97-digit number)
45845297800844808663…46126240405623579119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.584 Γ— 10⁹⁢(97-digit number)
45845297800844808663…46126240405623579121
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
9.169 Γ— 10⁹⁢(97-digit number)
91690595601689617326…92252480811247158239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.169 Γ— 10⁹⁢(97-digit number)
91690595601689617326…92252480811247158241
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
1.833 Γ— 10⁹⁷(98-digit number)
18338119120337923465…84504961622494316479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.833 Γ— 10⁹⁷(98-digit number)
18338119120337923465…84504961622494316481
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 491321

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 25bd7e9f29ee3cc12361991b8ff2e93453dffb85639d7da888edf58af1714b1e

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 #491,321 on Chainz β†—
Circulating Supply:57,754,717 XPMΒ·at block #6,813,830 Β· updates every 60s
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