XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #859,347

Block #859,347

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/19/2014, 9:27:36 AM Β· Difficulty 10.9655 Β· 5,966,882 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c6a76acef3c964f610f5f038c5be1757561e84f2ef8797385bdea4543e803a9b
View on Chainz β†—

Height

#859,347

Difficulty

10.965463

Transactions

1

Size

200 B

Version

2

Bits

0af72896

Nonce

1,621,822,879

Timestamp

12/19/2014, 9:27:36 AM

Confirmations

5,966,882

Merkle Root

b5268ad373cce0334a0fce0ac7e19d13e1fdb83cec472f1616a0be5b15e3597e
Transactions (1)
Coinbaseb5268ad373cce0…a0be5b15e3597e
1 in β†’ 1 out8.3000 XPM110 B
AakUtfVS…3JuNoUFo
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.

4.470 Γ— 10⁹³(94-digit number)
44702252859099396673…27318166619429903040
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
4.470 Γ— 10⁹³(94-digit number)
44702252859099396673…27318166619429903039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.470 Γ— 10⁹³(94-digit number)
44702252859099396673…27318166619429903041
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
8.940 Γ— 10⁹³(94-digit number)
89404505718198793346…54636333238859806079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.940 Γ— 10⁹³(94-digit number)
89404505718198793346…54636333238859806081
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
1.788 Γ— 10⁹⁴(95-digit number)
17880901143639758669…09272666477719612159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.788 Γ— 10⁹⁴(95-digit number)
17880901143639758669…09272666477719612161
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
3.576 Γ— 10⁹⁴(95-digit number)
35761802287279517338…18545332955439224319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.576 Γ— 10⁹⁴(95-digit number)
35761802287279517338…18545332955439224321
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
7.152 Γ— 10⁹⁴(95-digit number)
71523604574559034676…37090665910878448639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.152 Γ— 10⁹⁴(95-digit number)
71523604574559034676…37090665910878448641
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
1.430 Γ— 10⁹⁡(96-digit number)
14304720914911806935…74181331821756897279
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 859347

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 c6a76acef3c964f610f5f038c5be1757561e84f2ef8797385bdea4543e803a9b

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 #859,347 on Chainz β†—
Circulating Supply:57,853,966 XPMΒ·at block #6,826,228 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy