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Block #873,363

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/29/2014, 7:18:55 AM Β· Difficulty 10.9641 Β· 5,922,362 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
545e18aaf61d830c5e5afe4db30272dfd0d8fec1e8157593005f37438d28bbe1
View on Chainz β†—

Height

#873,363

Difficulty

10.964076

Transactions

1

Size

208 B

Version

2

Bits

0af6cda7

Nonce

2,325,336,190

Timestamp

12/29/2014, 7:18:55 AM

Confirmations

5,922,362

Merkle Root

29616479f84f60d5dfadf09c9e250657e81c4c4b654e9eb751d4062fea399e19
Transactions (1)
Coinbase29616479f84f60…d4062fea399e19
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
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.

9.112 Γ— 10⁹⁸(99-digit number)
91122807591468687056…72991740677011046400
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
9.112 Γ— 10⁹⁸(99-digit number)
91122807591468687056…72991740677011046399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.112 Γ— 10⁹⁸(99-digit number)
91122807591468687056…72991740677011046401
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
1.822 Γ— 10⁹⁹(100-digit number)
18224561518293737411…45983481354022092799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.822 Γ— 10⁹⁹(100-digit number)
18224561518293737411…45983481354022092801
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
3.644 Γ— 10⁹⁹(100-digit number)
36449123036587474822…91966962708044185599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.644 Γ— 10⁹⁹(100-digit number)
36449123036587474822…91966962708044185601
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
7.289 Γ— 10⁹⁹(100-digit number)
72898246073174949645…83933925416088371199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.289 Γ— 10⁹⁹(100-digit number)
72898246073174949645…83933925416088371201
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
1.457 Γ— 10¹⁰⁰(101-digit number)
14579649214634989929…67867850832176742399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.457 Γ— 10¹⁰⁰(101-digit number)
14579649214634989929…67867850832176742401
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 873363

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 545e18aaf61d830c5e5afe4db30272dfd0d8fec1e8157593005f37438d28bbe1

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 #873,363 on Chainz β†—
Circulating Supply:57,609,876 XPMΒ·at block #6,795,724 Β· updates every 60s
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