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Block #847,768

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/10/2014, 2:26:53 PM Β· Difficulty 10.9718 Β· 5,989,776 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
431effdf5738b4fc88b03a3d8cb7d109860cd997a142af0de5dcd32082234585
View on Chainz β†—

Height

#847,768

Difficulty

10.971796

Transactions

2

Size

431 B

Version

2

Bits

0af8c79f

Nonce

174,959,128

Timestamp

12/10/2014, 2:26:53 PM

Confirmations

5,989,776

Merkle Root

d9cd9c96439c9c324c1e3790fdbe947af0e49c00e8cf4350702e3eb60301b1ca
Transactions (2)
Coinbasec31bbc07f30f03…f1d9a5dbdf108d
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
5e98353af70680…3c9e067266ec9e
1 in β†’ 2 out6.9400 XPM225 B
AL7B788G…ntju5878ANbZfVir…5tx3bX4J
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.

7.468 Γ— 10⁹⁴(95-digit number)
74685790031973126059…29511485376693960880
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
7.468 Γ— 10⁹⁴(95-digit number)
74685790031973126059…29511485376693960879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.468 Γ— 10⁹⁴(95-digit number)
74685790031973126059…29511485376693960881
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
1.493 Γ— 10⁹⁡(96-digit number)
14937158006394625211…59022970753387921759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.493 Γ— 10⁹⁡(96-digit number)
14937158006394625211…59022970753387921761
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
2.987 Γ— 10⁹⁡(96-digit number)
29874316012789250423…18045941506775843519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.987 Γ— 10⁹⁡(96-digit number)
29874316012789250423…18045941506775843521
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
5.974 Γ— 10⁹⁡(96-digit number)
59748632025578500847…36091883013551687039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.974 Γ— 10⁹⁡(96-digit number)
59748632025578500847…36091883013551687041
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
1.194 Γ— 10⁹⁢(97-digit number)
11949726405115700169…72183766027103374079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.194 Γ— 10⁹⁢(97-digit number)
11949726405115700169…72183766027103374081
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 847768

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 431effdf5738b4fc88b03a3d8cb7d109860cd997a142af0de5dcd32082234585

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 #847,768 on Chainz β†—
Circulating Supply:57,944,680 XPMΒ·at block #6,837,543 Β· updates every 60s
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