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Block #163,856

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/14/2013, 7:02:01 AM Β· Difficulty 9.8619 Β· 6,641,263 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
07409e5e360b0b8a54b93dc84df39ff4769d6d8cea5473dca9bcfe5a1b32797e
View on Chainz β†—

Height

#163,856

Difficulty

9.861853

Transactions

1

Size

201 B

Version

2

Bits

09dca26a

Nonce

261,742

Timestamp

9/14/2013, 7:02:01 AM

Confirmations

6,641,263

Merkle Root

c7fa14e6b62c83fde9083d6eeec75b722fbdf4213c81f0e4d8d6f27b3ad5f36a
Transactions (1)
Coinbasec7fa14e6b62c83…d6f27b3ad5f36a
1 in β†’ 1 out10.2700 XPM109 B
AXJXpeT6…EkNjftUP
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.

3.326 Γ— 10⁹⁹(100-digit number)
33267128492119581027…15944370896454715200
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
3.326 Γ— 10⁹⁹(100-digit number)
33267128492119581027…15944370896454715199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.326 Γ— 10⁹⁹(100-digit number)
33267128492119581027…15944370896454715201
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
6.653 Γ— 10⁹⁹(100-digit number)
66534256984239162055…31888741792909430399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.653 Γ— 10⁹⁹(100-digit number)
66534256984239162055…31888741792909430401
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
1.330 Γ— 10¹⁰⁰(101-digit number)
13306851396847832411…63777483585818860799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.330 Γ— 10¹⁰⁰(101-digit number)
13306851396847832411…63777483585818860801
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
2.661 Γ— 10¹⁰⁰(101-digit number)
26613702793695664822…27554967171637721599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.661 Γ— 10¹⁰⁰(101-digit number)
26613702793695664822…27554967171637721601
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
5.322 Γ— 10¹⁰⁰(101-digit number)
53227405587391329644…55109934343275443199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 163856

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 07409e5e360b0b8a54b93dc84df39ff4769d6d8cea5473dca9bcfe5a1b32797e

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 #163,856 on Chainz β†—
Circulating Supply:57,685,022 XPMΒ·at block #6,805,118 Β· updates every 60s
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