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Home/Chain Registry/Block #1,612,624

Block #1,612,624

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/3/2016, 5:05:58 PM Β· Difficulty 10.6021 Β· 5,229,955 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c3e6844f08a39e7d53614d82acd87a6d9f63ed79bbab813b38624b127b467231
View on Chainz β†—

Difficulty

10.602140

Transactions

1

Size

199 B

Version

2

Bits

0a9a25d2

Nonce

893,984,840

Timestamp

6/3/2016, 5:05:58 PM

Confirmations

5,229,955

Merkle Root

087ac47ee1744d3d2684e89239dec63d1404e85bbc1c46068407a0320fa41998
Transactions (1)
Coinbase087ac47ee1744d…07a0320fa41998
1 in β†’ 1 out8.8800 XPM109 B
ARiYmCqg…ziNaaceQ
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.

2.908 Γ— 10⁹⁴(95-digit number)
29084367947942282095…33933254600530577160
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
2.908 Γ— 10⁹⁴(95-digit number)
29084367947942282095…33933254600530577159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.908 Γ— 10⁹⁴(95-digit number)
29084367947942282095…33933254600530577161
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
5.816 Γ— 10⁹⁴(95-digit number)
58168735895884564191…67866509201061154319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.816 Γ— 10⁹⁴(95-digit number)
58168735895884564191…67866509201061154321
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
1.163 Γ— 10⁹⁡(96-digit number)
11633747179176912838…35733018402122308639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.163 Γ— 10⁹⁡(96-digit number)
11633747179176912838…35733018402122308641
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
2.326 Γ— 10⁹⁡(96-digit number)
23267494358353825676…71466036804244617279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.326 Γ— 10⁹⁡(96-digit number)
23267494358353825676…71466036804244617281
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
4.653 Γ— 10⁹⁡(96-digit number)
46534988716707651352…42932073608489234559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.653 Γ— 10⁹⁡(96-digit number)
46534988716707651352…42932073608489234561
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 1612624

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 c3e6844f08a39e7d53614d82acd87a6d9f63ed79bbab813b38624b127b467231

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 #1,612,624 on Chainz β†—
Circulating Supply:57,985,060 XPMΒ·at block #6,842,578 Β· updates every 60s
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