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Block #59,729

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/18/2013, 3:57:19 AM Β· Difficulty 8.9662 Β· 6,746,023 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
33f1cbfb96ae4c7cefe313efe511a8dfa8438242a0008b5ca0a53181b688430f
View on Chainz β†—

Height

#59,729

Difficulty

8.966201

Transactions

2

Size

569 B

Version

2

Bits

08f758ed

Nonce

15

Timestamp

7/18/2013, 3:57:19 AM

Confirmations

6,746,023

Merkle Root

954a9457e5a262e52a461500b975180ed1096714fa02e84de2e547a1104d710b
Transactions (2)
Coinbase35cc79273e71c0…a3394ce8c73a21
1 in β†’ 1 out12.4300 XPM110 B
AKCeEpi5…ABjP77dd
8cff1872d9d81f…11739b553e5ec9
2 in β†’ 2 out108.8600 XPM373 B
AQnNKxxD…xyvGpsKYAaU3yEYr…w8AJttbc
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.

1.232 Γ— 10⁸⁡(86-digit number)
12321107129525966992…80797905455919035920
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
1.232 Γ— 10⁸⁡(86-digit number)
12321107129525966992…80797905455919035919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.232 Γ— 10⁸⁡(86-digit number)
12321107129525966992…80797905455919035921
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
2.464 Γ— 10⁸⁡(86-digit number)
24642214259051933985…61595810911838071839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.464 Γ— 10⁸⁡(86-digit number)
24642214259051933985…61595810911838071841
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
4.928 Γ— 10⁸⁡(86-digit number)
49284428518103867971…23191621823676143679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.928 Γ— 10⁸⁡(86-digit number)
49284428518103867971…23191621823676143681
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
9.856 Γ— 10⁸⁡(86-digit number)
98568857036207735943…46383243647352287359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.856 Γ— 10⁸⁡(86-digit number)
98568857036207735943…46383243647352287361
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
1.971 Γ— 10⁸⁢(87-digit number)
19713771407241547188…92766487294704574719
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 59729

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 33f1cbfb96ae4c7cefe313efe511a8dfa8438242a0008b5ca0a53181b688430f

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 #59,729 on Chainz β†—
Circulating Supply:57,690,097 XPMΒ·at block #6,805,751 Β· updates every 60s
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