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Block #153,589

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/7/2013, 2:52:11 AM Β· Difficulty 9.8632 Β· 6,672,986 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
35c68b0f6e0db9cd707e81ca2ccca6cd9a5252ee5ebf9a8c155322ebb03bc52e
View on Chainz β†—

Height

#153,589

Difficulty

9.863224

Transactions

1

Size

199 B

Version

2

Bits

09dcfc42

Nonce

769,084

Timestamp

9/7/2013, 2:52:11 AM

Confirmations

6,672,986

Merkle Root

0901fdea354afbe8f4f19532fa016fa3b8c0fff313b3a5346df367a919d3e482
Transactions (1)
Coinbase0901fdea354afb…f367a919d3e482
1 in β†’ 1 out10.2600 XPM109 B
AQd6aVp2…1bi6snDv
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.

4.104 Γ— 10⁹⁡(96-digit number)
41049943129553372858…50456643544043899880
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
4.104 Γ— 10⁹⁡(96-digit number)
41049943129553372858…50456643544043899879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.104 Γ— 10⁹⁡(96-digit number)
41049943129553372858…50456643544043899881
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
8.209 Γ— 10⁹⁡(96-digit number)
82099886259106745717…00913287088087799759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.209 Γ— 10⁹⁡(96-digit number)
82099886259106745717…00913287088087799761
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
1.641 Γ— 10⁹⁢(97-digit number)
16419977251821349143…01826574176175599519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.641 Γ— 10⁹⁢(97-digit number)
16419977251821349143…01826574176175599521
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
3.283 Γ— 10⁹⁢(97-digit number)
32839954503642698287…03653148352351199039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.283 Γ— 10⁹⁢(97-digit number)
32839954503642698287…03653148352351199041
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
6.567 Γ— 10⁹⁢(97-digit number)
65679909007285396574…07306296704702398079
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 153589

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 35c68b0f6e0db9cd707e81ca2ccca6cd9a5252ee5ebf9a8c155322ebb03bc52e

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 #153,589 on Chainz β†—
Circulating Supply:57,856,749 XPMΒ·at block #6,826,574 Β· updates every 60s
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