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Block #845,128

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/8/2014, 3:50:29 PM Β· Difficulty 10.9726 Β· 5,986,942 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1cec525126cf83a2257de0fa26a6930b23bf1b2a2a0b5e446fcf1cb2b39b92c9
View on Chainz β†—

Height

#845,128

Difficulty

10.972584

Transactions

1

Size

243 B

Version

2

Bits

0af8fb40

Nonce

1,551,685,771

Timestamp

12/8/2014, 3:50:29 PM

Confirmations

5,986,942

Merkle Root

bcac918bac850629d96f34182aec33b8224c8b2427642bd5f9f7daecd91b91f7
Transactions (1)
Coinbasebcac918bac8506…f7daecd91b91f7
1 in β†’ 2 out8.2900 XPM152 B
AYK1QFZ4…PR5iJU9QALPu3s2c…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.

2.346 Γ— 10⁹⁷(98-digit number)
23462559020795275725…90116499696479518720
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
2.346 Γ— 10⁹⁷(98-digit number)
23462559020795275725…90116499696479518719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.346 Γ— 10⁹⁷(98-digit number)
23462559020795275725…90116499696479518721
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
4.692 Γ— 10⁹⁷(98-digit number)
46925118041590551451…80232999392959037439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.692 Γ— 10⁹⁷(98-digit number)
46925118041590551451…80232999392959037441
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
9.385 Γ— 10⁹⁷(98-digit number)
93850236083181102903…60465998785918074879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.385 Γ— 10⁹⁷(98-digit number)
93850236083181102903…60465998785918074881
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
1.877 Γ— 10⁹⁸(99-digit number)
18770047216636220580…20931997571836149759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.877 Γ— 10⁹⁸(99-digit number)
18770047216636220580…20931997571836149761
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
3.754 Γ— 10⁹⁸(99-digit number)
37540094433272441161…41863995143672299519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.754 Γ— 10⁹⁸(99-digit number)
37540094433272441161…41863995143672299521
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 845128

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 1cec525126cf83a2257de0fa26a6930b23bf1b2a2a0b5e446fcf1cb2b39b92c9

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 #845,128 on Chainz β†—
Circulating Supply:57,900,685 XPMΒ·at block #6,832,069 Β· updates every 60s
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