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Home/Chain Registry/Block #1,631,321

Block #1,631,321

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/16/2016, 4:47:22 PM Β· Difficulty 10.6026 Β· 5,211,313 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6cfd7b2f0bc0e52ccee8db74ca2d3b7da2e137fdba9af85bd97fd52f742fa7e6
View on Chainz β†—

Difficulty

10.602585

Transactions

1

Size

199 B

Version

2

Bits

0a9a4305

Nonce

153,498,297

Timestamp

6/16/2016, 4:47:22 PM

Confirmations

5,211,313

Merkle Root

66d8d7e7a18162f402b8e1e9595b90586bece9df28ea58ade839b14ce332d461
Transactions (1)
Coinbase66d8d7e7a18162…39b14ce332d461
1 in β†’ 1 out8.8800 XPM110 B
AeA8Cj7o…7B8H1p9r
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.

1.508 Γ— 10⁹²(93-digit number)
15085722429822479551…41446902165091046840
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
1.508 Γ— 10⁹²(93-digit number)
15085722429822479551…41446902165091046839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.508 Γ— 10⁹²(93-digit number)
15085722429822479551…41446902165091046841
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
3.017 Γ— 10⁹²(93-digit number)
30171444859644959103…82893804330182093679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.017 Γ— 10⁹²(93-digit number)
30171444859644959103…82893804330182093681
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
6.034 Γ— 10⁹²(93-digit number)
60342889719289918206…65787608660364187359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.034 Γ— 10⁹²(93-digit number)
60342889719289918206…65787608660364187361
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
1.206 Γ— 10⁹³(94-digit number)
12068577943857983641…31575217320728374719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.206 Γ— 10⁹³(94-digit number)
12068577943857983641…31575217320728374721
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
2.413 Γ— 10⁹³(94-digit number)
24137155887715967282…63150434641456749439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.413 Γ— 10⁹³(94-digit number)
24137155887715967282…63150434641456749441
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 1631321

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 6cfd7b2f0bc0e52ccee8db74ca2d3b7da2e137fdba9af85bd97fd52f742fa7e6

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 #1,631,321 on Chainz β†—
Circulating Supply:57,985,505 XPMΒ·at block #6,842,633 Β· updates every 60s
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