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Home/Chain Registry/Block #1,631,323

Block #1,631,323

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/16/2016, 4:48:23 PM Β· Difficulty 10.6027 Β· 5,207,590 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5d6bf50679fb23b87ee42d3e94d177c804c8d3bd4a06c05d8e3366edd830f85d
View on Chainz β†—

Difficulty

10.602656

Transactions

1

Size

200 B

Version

2

Bits

0a9a47ac

Nonce

561,489,251

Timestamp

6/16/2016, 4:48:23 PM

Confirmations

5,207,590

Merkle Root

953200c936f0de555e4dbad3b9ae4042231495fbc5f52e5c5f9799e77ca49dfb
Transactions (1)
Coinbase953200c936f0de…9799e77ca49dfb
1 in β†’ 1 out8.8800 XPM110 B
AdpUvHUy…wmnDRuTz
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.

3.467 Γ— 10⁹⁡(96-digit number)
34674797676936976105…33736215773032243840
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
3.467 Γ— 10⁹⁡(96-digit number)
34674797676936976105…33736215773032243839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.467 Γ— 10⁹⁡(96-digit number)
34674797676936976105…33736215773032243841
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
6.934 Γ— 10⁹⁡(96-digit number)
69349595353873952211…67472431546064487679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.934 Γ— 10⁹⁡(96-digit number)
69349595353873952211…67472431546064487681
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
1.386 Γ— 10⁹⁢(97-digit number)
13869919070774790442…34944863092128975359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.386 Γ— 10⁹⁢(97-digit number)
13869919070774790442…34944863092128975361
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
2.773 Γ— 10⁹⁢(97-digit number)
27739838141549580884…69889726184257950719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.773 Γ— 10⁹⁢(97-digit number)
27739838141549580884…69889726184257950721
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
5.547 Γ— 10⁹⁢(97-digit number)
55479676283099161769…39779452368515901439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.547 Γ— 10⁹⁢(97-digit number)
55479676283099161769…39779452368515901441
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 1631323

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 5d6bf50679fb23b87ee42d3e94d177c804c8d3bd4a06c05d8e3366edd830f85d

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 #1,631,323 on Chainz β†—
Circulating Supply:57,955,564 XPMΒ·at block #6,838,912 Β· updates every 60s
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