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Block #932,729

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/12/2015, 3:16:38 AM Β· Difficulty 10.9027 Β· 5,881,755 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2fb8df24f28e8432a6a3c903f6cd63f070fab041bba1087d5fa01c52b1f1c706
View on Chainz β†—

Height

#932,729

Difficulty

10.902661

Transactions

1

Size

242 B

Version

2

Bits

0ae714ce

Nonce

927,526,592

Timestamp

2/12/2015, 3:16:38 AM

Confirmations

5,881,755

Merkle Root

fac0bd9e71327295344cffc92b511a9e092f89594a84f1fd4e3378e8842f6629
Transactions (1)
Coinbasefac0bd9e713272…3378e8842f6629
1 in β†’ 2 out8.4000 XPM152 B
AP7y578F…8eJ8kdV3ALPu3s2c…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.

1.889 Γ— 10⁹⁡(96-digit number)
18891567955899464401…93063709185280971760
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
1.889 Γ— 10⁹⁡(96-digit number)
18891567955899464401…93063709185280971759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.889 Γ— 10⁹⁡(96-digit number)
18891567955899464401…93063709185280971761
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
3.778 Γ— 10⁹⁡(96-digit number)
37783135911798928803…86127418370561943519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.778 Γ— 10⁹⁡(96-digit number)
37783135911798928803…86127418370561943521
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
7.556 Γ— 10⁹⁡(96-digit number)
75566271823597857606…72254836741123887039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.556 Γ— 10⁹⁡(96-digit number)
75566271823597857606…72254836741123887041
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
1.511 Γ— 10⁹⁢(97-digit number)
15113254364719571521…44509673482247774079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.511 Γ— 10⁹⁢(97-digit number)
15113254364719571521…44509673482247774081
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
3.022 Γ— 10⁹⁢(97-digit number)
30226508729439143042…89019346964495548159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.022 Γ— 10⁹⁢(97-digit number)
30226508729439143042…89019346964495548161
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 932729

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 2fb8df24f28e8432a6a3c903f6cd63f070fab041bba1087d5fa01c52b1f1c706

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 #932,729 on Chainz β†—
Circulating Supply:57,759,940 XPMΒ·at block #6,814,483 Β· updates every 60s
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