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Home/Chain Registry/Block #1,406,638

Block #1,406,638

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/10/2016, 1:03:23 AM Β· Difficulty 10.8066 Β· 5,438,197 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
46af6e0a253824d26f5461d876f090786fd2fc32d0af234535fb5ce1cccf2f93
View on Chainz β†—

Difficulty

10.806619

Transactions

1

Size

243 B

Version

2

Bits

0ace7e9d

Nonce

1,765,496,795

Timestamp

1/10/2016, 1:03:23 AM

Confirmations

5,438,197

Merkle Root

3ac9275dfe78335b0920bcf0a949848e6cd3fba51ae17c6c1c1896aa32960869
Transactions (1)
Coinbase3ac9275dfe7833…1896aa32960869
1 in β†’ 2 out8.5500 XPM152 B
AbNVgXWJ…g3uNfMnjALPu3s2c…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.

7.159 Γ— 10⁹⁷(98-digit number)
71597855550833027640…06556658554226851840
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
7.159 Γ— 10⁹⁷(98-digit number)
71597855550833027640…06556658554226851839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.159 Γ— 10⁹⁷(98-digit number)
71597855550833027640…06556658554226851841
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
1.431 Γ— 10⁹⁸(99-digit number)
14319571110166605528…13113317108453703679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.431 Γ— 10⁹⁸(99-digit number)
14319571110166605528…13113317108453703681
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
2.863 Γ— 10⁹⁸(99-digit number)
28639142220333211056…26226634216907407359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.863 Γ— 10⁹⁸(99-digit number)
28639142220333211056…26226634216907407361
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
5.727 Γ— 10⁹⁸(99-digit number)
57278284440666422112…52453268433814814719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.727 Γ— 10⁹⁸(99-digit number)
57278284440666422112…52453268433814814721
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
1.145 Γ— 10⁹⁹(100-digit number)
11455656888133284422…04906536867629629439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.145 Γ— 10⁹⁹(100-digit number)
11455656888133284422…04906536867629629441
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 1406638

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 46af6e0a253824d26f5461d876f090786fd2fc32d0af234535fb5ce1cccf2f93

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 #1,406,638 on Chainz β†—
Circulating Supply:58,003,088 XPMΒ·at block #6,844,834 Β· updates every 60s
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