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Block #892,568

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/12/2015, 4:49:23 PM Β· Difficulty 10.9521 Β· 5,932,439 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
09b7b71a3b5d226aaa49f4eeaedfcd780dac8390061e4448f085133df2fa9116
View on Chainz β†—

Height

#892,568

Difficulty

10.952088

Transactions

1

Size

207 B

Version

2

Bits

0af3bc0e

Nonce

505,919,334

Timestamp

1/12/2015, 4:49:23 PM

Confirmations

5,932,439

Merkle Root

e053329ba73320ec45d34ccd8bcb9735900d25dc6d583f17df3fd63b745f6a18
Transactions (1)
Coinbasee053329ba73320…3fd63b745f6a18
1 in β†’ 1 out8.3200 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.

7.320 Γ— 10⁹⁢(97-digit number)
73203868199674179622…24321577778071618560
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
7.320 Γ— 10⁹⁢(97-digit number)
73203868199674179622…24321577778071618559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.320 Γ— 10⁹⁢(97-digit number)
73203868199674179622…24321577778071618561
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
1.464 Γ— 10⁹⁷(98-digit number)
14640773639934835924…48643155556143237119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.464 Γ— 10⁹⁷(98-digit number)
14640773639934835924…48643155556143237121
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
2.928 Γ— 10⁹⁷(98-digit number)
29281547279869671849…97286311112286474239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.928 Γ— 10⁹⁷(98-digit number)
29281547279869671849…97286311112286474241
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
5.856 Γ— 10⁹⁷(98-digit number)
58563094559739343698…94572622224572948479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.856 Γ— 10⁹⁷(98-digit number)
58563094559739343698…94572622224572948481
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
1.171 Γ— 10⁹⁸(99-digit number)
11712618911947868739…89145244449145896959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.171 Γ— 10⁹⁸(99-digit number)
11712618911947868739…89145244449145896961
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
2.342 Γ— 10⁹⁸(99-digit number)
23425237823895737479…78290488898291793919
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 892568

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 09b7b71a3b5d226aaa49f4eeaedfcd780dac8390061e4448f085133df2fa9116

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 #892,568 on Chainz β†—
Circulating Supply:57,844,140 XPMΒ·at block #6,825,006 Β· updates every 60s
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