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Block #567,275

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/29/2014, 3:06:10 PM Β· Difficulty 10.9649 Β· 6,249,721 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a890f02230be0943388a24fb8bf3fc862df7c1f8faef4bb1544e0d7854268be9
View on Chainz β†—

Height

#567,275

Difficulty

10.964853

Transactions

2

Size

433 B

Version

2

Bits

0af70099

Nonce

460,855,462

Timestamp

5/29/2014, 3:06:10 PM

Confirmations

6,249,721

Merkle Root

4b059178c9527108dedbe4917cd77c41a18e568182e119534d055aef801d2f78
Transactions (2)
Coinbase43b146a1f9c3c7…353031f6760652
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
a862e81740f77d…8bc5a91dffb11e
1 in β†’ 2 out5.3098 XPM226 B
AeKNrjNj…1NEq95TaAcBvLaSu…X3gaHvJ1
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.

1.150 Γ— 10⁹⁸(99-digit number)
11502641925934007674…09221251430019089920
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
1.150 Γ— 10⁹⁸(99-digit number)
11502641925934007674…09221251430019089919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.150 Γ— 10⁹⁸(99-digit number)
11502641925934007674…09221251430019089921
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
2.300 Γ— 10⁹⁸(99-digit number)
23005283851868015349…18442502860038179839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.300 Γ— 10⁹⁸(99-digit number)
23005283851868015349…18442502860038179841
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
4.601 Γ— 10⁹⁸(99-digit number)
46010567703736030698…36885005720076359679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.601 Γ— 10⁹⁸(99-digit number)
46010567703736030698…36885005720076359681
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
9.202 Γ— 10⁹⁸(99-digit number)
92021135407472061397…73770011440152719359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.202 Γ— 10⁹⁸(99-digit number)
92021135407472061397…73770011440152719361
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
1.840 Γ— 10⁹⁹(100-digit number)
18404227081494412279…47540022880305438719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.840 Γ— 10⁹⁹(100-digit number)
18404227081494412279…47540022880305438721
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
3.680 Γ— 10⁹⁹(100-digit number)
36808454162988824559…95080045760610877439
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 567275

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 a890f02230be0943388a24fb8bf3fc862df7c1f8faef4bb1544e0d7854268be9

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 #567,275 on Chainz β†—
Circulating Supply:57,779,999 XPMΒ·at block #6,816,995 Β· updates every 60s
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