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Block #287,064

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/1/2013, 4:04:37 AM Β· Difficulty 9.9863 Β· 6,509,282 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8d65d13beef1bf27c6b3fd40d25113953155d7ba3d0f43962ddfa53f421195c7
View on Chainz β†—

Height

#287,064

Difficulty

9.986276

Transactions

1

Size

210 B

Version

2

Bits

09fc7c91

Nonce

117,443,844

Timestamp

12/1/2013, 4:04:37 AM

Confirmations

6,509,282

Merkle Root

9594f61e0ece08b2b92fe30fad2e671bee66ab763c9a1e40def1277ae2eb01ac
Transactions (1)
Coinbase9594f61e0ece08…f1277ae2eb01ac
1 in β†’ 1 out10.0100 XPM116 B
AcLBm5Z9…S683d7c3
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.

5.275 Γ— 10¹⁰³(104-digit number)
52755272260189225521…34087562289356694100
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
5.275 Γ— 10¹⁰³(104-digit number)
52755272260189225521…34087562289356694099
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.275 Γ— 10¹⁰³(104-digit number)
52755272260189225521…34087562289356694101
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
1.055 Γ— 10¹⁰⁴(105-digit number)
10551054452037845104…68175124578713388199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.055 Γ— 10¹⁰⁴(105-digit number)
10551054452037845104…68175124578713388201
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
2.110 Γ— 10¹⁰⁴(105-digit number)
21102108904075690208…36350249157426776399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.110 Γ— 10¹⁰⁴(105-digit number)
21102108904075690208…36350249157426776401
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
4.220 Γ— 10¹⁰⁴(105-digit number)
42204217808151380416…72700498314853552799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.220 Γ— 10¹⁰⁴(105-digit number)
42204217808151380416…72700498314853552801
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
8.440 Γ— 10¹⁰⁴(105-digit number)
84408435616302760833…45400996629707105599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.440 Γ— 10¹⁰⁴(105-digit number)
84408435616302760833…45400996629707105601
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 287064

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 8d65d13beef1bf27c6b3fd40d25113953155d7ba3d0f43962ddfa53f421195c7

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 #287,064 on Chainz β†—
Circulating Supply:57,614,761 XPMΒ·at block #6,796,345 Β· updates every 60s
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