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Block #531,133

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/8/2014, 7:46:33 AM Β· Difficulty 10.8934 Β· 6,264,257 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cd6bb70f2b1d619e536bfe9a2dd73f3a4ad06fcd5a742d34c7054aa72ad7f38c
View on Chainz β†—

Height

#531,133

Difficulty

10.893448

Transactions

3

Size

959 B

Version

2

Bits

0ae4b909

Nonce

51,654,602

Timestamp

5/8/2014, 7:46:33 AM

Confirmations

6,264,257

Merkle Root

36f2611ae63ca59f1e774b2ae634f558b9413f5a17b9bca78e4bf8c6bbf38a00
Transactions (3)
Coinbase7350d04ebd6522…7c8750a656dbeb
1 in β†’ 1 out8.4300 XPM116 B
ANSXnLY2…Sd25TjkD
492e28fdd49956…4b712438c0809b
3 in β†’ 2 out25.3300 XPM525 B
AQ6HeNTK…jgwW2QVzAaUNi76B…wtcm5mLM
fe81665d63802f…d3f702cbf44092
1 in β†’ 2 out1.3473 XPM226 B
AZUm9GX6…tZ5dn1V6AdGaEuE4…4fB5D786
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.

8.424 Γ— 10⁹⁸(99-digit number)
84249164084192623718…99854763016835984560
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
8.424 Γ— 10⁹⁸(99-digit number)
84249164084192623718…99854763016835984559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.424 Γ— 10⁹⁸(99-digit number)
84249164084192623718…99854763016835984561
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
1.684 Γ— 10⁹⁹(100-digit number)
16849832816838524743…99709526033671969119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.684 Γ— 10⁹⁹(100-digit number)
16849832816838524743…99709526033671969121
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
3.369 Γ— 10⁹⁹(100-digit number)
33699665633677049487…99419052067343938239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.369 Γ— 10⁹⁹(100-digit number)
33699665633677049487…99419052067343938241
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
6.739 Γ— 10⁹⁹(100-digit number)
67399331267354098974…98838104134687876479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.739 Γ— 10⁹⁹(100-digit number)
67399331267354098974…98838104134687876481
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
1.347 Γ— 10¹⁰⁰(101-digit number)
13479866253470819794…97676208269375752959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.347 Γ— 10¹⁰⁰(101-digit number)
13479866253470819794…97676208269375752961
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 531133

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 cd6bb70f2b1d619e536bfe9a2dd73f3a4ad06fcd5a742d34c7054aa72ad7f38c

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 #531,133 on Chainz β†—
Circulating Supply:57,607,180 XPMΒ·at block #6,795,389 Β· updates every 60s
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