XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #862,097

Block #862,097

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/21/2014, 11:44:42 AM Β· Difficulty 10.9637 Β· 5,976,485 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bff8ef3b011ffdd091d832eec293e803dc4bfc55836ee6d6b0cabfe880593ce3
View on Chainz β†—

Height

#862,097

Difficulty

10.963659

Transactions

1

Size

207 B

Version

2

Bits

0af6b25d

Nonce

119,588,424

Timestamp

12/21/2014, 11:44:42 AM

Confirmations

5,976,485

Merkle Root

849bbaebe90d0c473414ec8528a0bf8eddbc9cab24b9373a09f014612f29b618
Transactions (1)
Coinbase849bbaebe90d0c…f014612f29b618
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.

2.893 Γ— 10⁹⁷(98-digit number)
28933756565677754556…14592020267876188160
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
2.893 Γ— 10⁹⁷(98-digit number)
28933756565677754556…14592020267876188159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.893 Γ— 10⁹⁷(98-digit number)
28933756565677754556…14592020267876188161
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
5.786 Γ— 10⁹⁷(98-digit number)
57867513131355509113…29184040535752376319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.786 Γ— 10⁹⁷(98-digit number)
57867513131355509113…29184040535752376321
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
1.157 Γ— 10⁹⁸(99-digit number)
11573502626271101822…58368081071504752639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.157 Γ— 10⁹⁸(99-digit number)
11573502626271101822…58368081071504752641
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
2.314 Γ— 10⁹⁸(99-digit number)
23147005252542203645…16736162143009505279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.314 Γ— 10⁹⁸(99-digit number)
23147005252542203645…16736162143009505281
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
4.629 Γ— 10⁹⁸(99-digit number)
46294010505084407291…33472324286019010559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.629 Γ— 10⁹⁸(99-digit number)
46294010505084407291…33472324286019010561
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 862097

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 bff8ef3b011ffdd091d832eec293e803dc4bfc55836ee6d6b0cabfe880593ce3

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 #862,097 on Chainz β†—
Circulating Supply:57,952,941 XPMΒ·at block #6,838,581 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