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Block #133,760

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/25/2013, 5:07:39 PM Β· Difficulty 9.7969 Β· 6,691,674 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7635b7155125eec4f478e0ae123f95815020b3f95e6e95a27cb27288937456e6
View on Chainz β†—

Height

#133,760

Difficulty

9.796888

Transactions

1

Size

201 B

Version

2

Bits

09cc00d6

Nonce

122,862

Timestamp

8/25/2013, 5:07:39 PM

Confirmations

6,691,674

Merkle Root

ea52ddfe5dd5f7ee29656eace51a17861bf7ccfc8b3593fe8c7a3b541bdbfacd
Transactions (1)
Coinbaseea52ddfe5dd5f7…7a3b541bdbfacd
1 in β†’ 1 out10.4000 XPM109 B
AetpQsvW…BEePeKKm
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.

1.893 Γ— 10⁹⁹(100-digit number)
18935586119071016569…06018842036388450400
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
1.893 Γ— 10⁹⁹(100-digit number)
18935586119071016569…06018842036388450399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.893 Γ— 10⁹⁹(100-digit number)
18935586119071016569…06018842036388450401
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
3.787 Γ— 10⁹⁹(100-digit number)
37871172238142033139…12037684072776900799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.787 Γ— 10⁹⁹(100-digit number)
37871172238142033139…12037684072776900801
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
7.574 Γ— 10⁹⁹(100-digit number)
75742344476284066279…24075368145553801599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.574 Γ— 10⁹⁹(100-digit number)
75742344476284066279…24075368145553801601
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
1.514 Γ— 10¹⁰⁰(101-digit number)
15148468895256813255…48150736291107603199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.514 Γ— 10¹⁰⁰(101-digit number)
15148468895256813255…48150736291107603201
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
3.029 Γ— 10¹⁰⁰(101-digit number)
30296937790513626511…96301472582215206399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.029 Γ— 10¹⁰⁰(101-digit number)
30296937790513626511…96301472582215206401
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 133760

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 7635b7155125eec4f478e0ae123f95815020b3f95e6e95a27cb27288937456e6

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 #133,760 on Chainz β†—
Circulating Supply:57,847,575 XPMΒ·at block #6,825,433 Β· updates every 60s
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