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Block #860,812

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/20/2014, 1:24:46 PM Β· Difficulty 10.9640 Β· 5,966,293 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
687e328a4ea16fa1ae8b9541d6b42f994682fbada8a4875323375b6800591240
View on Chainz β†—

Height

#860,812

Difficulty

10.964012

Transactions

2

Size

4.33 KB

Version

2

Bits

0af6c97a

Nonce

321,445,970

Timestamp

12/20/2014, 1:24:46 PM

Confirmations

5,966,293

Merkle Root

6b3be2cbd620cdef565fb611a5540da4b004e9bc192a6ac5bbb4e452f075e0ed
Transactions (2)
Coinbase3879ae1e8f9e8d…6a29078f6abc5f
1 in β†’ 1 out8.3600 XPM116 B
ANSXnLY2…Sd25TjkD
d1e836fb36bebf…27bc07112bab6e
28 in β†’ 2 out182.2543 XPM4.12 KB
AbHHErCb…o2AwhsZxAXCd1ktx…XsFCqMA8
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.

1.981 Γ— 10⁹⁢(97-digit number)
19819746725152785424…02753905516148333200
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
1.981 Γ— 10⁹⁢(97-digit number)
19819746725152785424…02753905516148333199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.981 Γ— 10⁹⁢(97-digit number)
19819746725152785424…02753905516148333201
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
3.963 Γ— 10⁹⁢(97-digit number)
39639493450305570849…05507811032296666399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.963 Γ— 10⁹⁢(97-digit number)
39639493450305570849…05507811032296666401
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
7.927 Γ— 10⁹⁢(97-digit number)
79278986900611141698…11015622064593332799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.927 Γ— 10⁹⁢(97-digit number)
79278986900611141698…11015622064593332801
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
1.585 Γ— 10⁹⁷(98-digit number)
15855797380122228339…22031244129186665599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.585 Γ— 10⁹⁷(98-digit number)
15855797380122228339…22031244129186665601
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
3.171 Γ— 10⁹⁷(98-digit number)
31711594760244456679…44062488258373331199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.171 Γ— 10⁹⁷(98-digit number)
31711594760244456679…44062488258373331201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
6.342 Γ— 10⁹⁷(98-digit number)
63423189520488913358…88124976516746662399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 860812

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 687e328a4ea16fa1ae8b9541d6b42f994682fbada8a4875323375b6800591240

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 #860,812 on Chainz β†—
Circulating Supply:57,861,018 XPMΒ·at block #6,827,104 Β· updates every 60s
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