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Block #271,816

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/24/2013, 8:40:26 PM Β· Difficulty 9.9525 Β· 6,523,889 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7572e1e1c4e13b8bdb4e18154592073261af2171d387c0143bd789584eb00b4c
View on Chainz β†—

Height

#271,816

Difficulty

9.952471

Transactions

1

Size

185 B

Version

2

Bits

09f3d520

Nonce

154,411

Timestamp

11/24/2013, 8:40:26 PM

Confirmations

6,523,889

Merkle Root

949d0ff806311783912979096e2a5152896b45aff3c93163a2e0468f4fdfed02
Transactions (1)
Coinbase949d0ff8063117…e0468f4fdfed02
1 in β†’ 1 out10.0800 XPM97 B
AQKLJgF6…zYGibgy9
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.

2.670 Γ— 10⁹⁰(91-digit number)
26708194393219402584…87166312915666122080
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
2.670 Γ— 10⁹⁰(91-digit number)
26708194393219402584…87166312915666122079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.670 Γ— 10⁹⁰(91-digit number)
26708194393219402584…87166312915666122081
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
5.341 Γ— 10⁹⁰(91-digit number)
53416388786438805168…74332625831332244159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.341 Γ— 10⁹⁰(91-digit number)
53416388786438805168…74332625831332244161
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
1.068 Γ— 10⁹¹(92-digit number)
10683277757287761033…48665251662664488319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.068 Γ— 10⁹¹(92-digit number)
10683277757287761033…48665251662664488321
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
2.136 Γ— 10⁹¹(92-digit number)
21366555514575522067…97330503325328976639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.136 Γ— 10⁹¹(92-digit number)
21366555514575522067…97330503325328976641
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
4.273 Γ— 10⁹¹(92-digit number)
42733111029151044134…94661006650657953279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.273 Γ— 10⁹¹(92-digit number)
42733111029151044134…94661006650657953281
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 271816

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 7572e1e1c4e13b8bdb4e18154592073261af2171d387c0143bd789584eb00b4c

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 #271,816 on Chainz β†—
Circulating Supply:57,609,712 XPMΒ·at block #6,795,704 Β· updates every 60s
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