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Block #141,533

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/30/2013, 9:26:19 AM Β· Difficulty 9.8348 Β· 6,653,344 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ce68049e4e4e5b47286b80c1237edfbb5379b5d52737d86484ca3b8fd576a3ea
View on Chainz β†—

Height

#141,533

Difficulty

9.834771

Transactions

1

Size

198 B

Version

2

Bits

09d5b394

Nonce

102,620

Timestamp

8/30/2013, 9:26:19 AM

Confirmations

6,653,344

Merkle Root

290945e643b3b02f2b58758d7e017bd9231b284fd409d28eb78cd149f028d3ae
Transactions (1)
Coinbase290945e643b3b0…8cd149f028d3ae
1 in β†’ 1 out10.3200 XPM109 B
AKzPUWKY…RHfPYGVa
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.

5.144 Γ— 10⁹²(93-digit number)
51447931316635594419…16050778481748656400
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
5.144 Γ— 10⁹²(93-digit number)
51447931316635594419…16050778481748656399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.144 Γ— 10⁹²(93-digit number)
51447931316635594419…16050778481748656401
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
1.028 Γ— 10⁹³(94-digit number)
10289586263327118883…32101556963497312799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.028 Γ— 10⁹³(94-digit number)
10289586263327118883…32101556963497312801
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
2.057 Γ— 10⁹³(94-digit number)
20579172526654237767…64203113926994625599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.057 Γ— 10⁹³(94-digit number)
20579172526654237767…64203113926994625601
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
4.115 Γ— 10⁹³(94-digit number)
41158345053308475535…28406227853989251199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.115 Γ— 10⁹³(94-digit number)
41158345053308475535…28406227853989251201
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
8.231 Γ— 10⁹³(94-digit number)
82316690106616951070…56812455707978502399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.231 Γ— 10⁹³(94-digit number)
82316690106616951070…56812455707978502401
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 141533

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 ce68049e4e4e5b47286b80c1237edfbb5379b5d52737d86484ca3b8fd576a3ea

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 #141,533 on Chainz β†—
Circulating Supply:57,603,050 XPMΒ·at block #6,794,876 Β· updates every 60s
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