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Block #683,014

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/18/2014, 6:08:56 PM Β· Difficulty 10.9600 Β· 6,142,305 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d263b7e0ee84fbf26a452a14b310c8361b1d3df75a222815ce220ff7758873ec
View on Chainz β†—

Height

#683,014

Difficulty

10.959959

Transactions

1

Size

243 B

Version

2

Bits

0af5bfe2

Nonce

1,559,020,967

Timestamp

8/18/2014, 6:08:56 PM

Confirmations

6,142,305

Merkle Root

371678237de87eccd7e3278997e514853c92c7023c8019682720dca5e12979fd
Transactions (1)
Coinbase371678237de87e…20dca5e12979fd
1 in β†’ 2 out8.3100 XPM152 B
ATrzKxLE…dnfypiwkALPu3s2c…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.

1.347 Γ— 10⁹⁢(97-digit number)
13473336871716010493…06535113554460400000
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
1.347 Γ— 10⁹⁢(97-digit number)
13473336871716010493…06535113554460399999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.347 Γ— 10⁹⁢(97-digit number)
13473336871716010493…06535113554460400001
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
2.694 Γ— 10⁹⁢(97-digit number)
26946673743432020987…13070227108920799999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.694 Γ— 10⁹⁢(97-digit number)
26946673743432020987…13070227108920800001
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
5.389 Γ— 10⁹⁢(97-digit number)
53893347486864041975…26140454217841599999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.389 Γ— 10⁹⁢(97-digit number)
53893347486864041975…26140454217841600001
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
1.077 Γ— 10⁹⁷(98-digit number)
10778669497372808395…52280908435683199999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.077 Γ— 10⁹⁷(98-digit number)
10778669497372808395…52280908435683200001
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
2.155 Γ— 10⁹⁷(98-digit number)
21557338994745616790…04561816871366399999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.155 Γ— 10⁹⁷(98-digit number)
21557338994745616790…04561816871366400001
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 683014

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 d263b7e0ee84fbf26a452a14b310c8361b1d3df75a222815ce220ff7758873ec

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 #683,014 on Chainz β†—
Circulating Supply:57,846,656 XPMΒ·at block #6,825,318 Β· updates every 60s
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