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Block #32,519

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 2:56:07 AM Β· Difficulty 7.9905 Β· 6,781,791 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a629fa7bfb89ce1afad877252b7d41321dc475de5a561106e6b4f41d90d8a9a0
View on Chainz β†—

Height

#32,519

Difficulty

7.990515

Transactions

2

Size

390 B

Version

2

Bits

07fd9263

Nonce

377

Timestamp

7/14/2013, 2:56:07 AM

Confirmations

6,781,791

Merkle Root

063dfc9d5a1a0a6f8e8dc5b9ac14c21fd8c194a90ccfdff2c36ebf211df769e6
Transactions (2)
Coinbase17909e80e4eafc…beb81e3a39185a
1 in β†’ 1 out15.6500 XPM108 B
AV6P7enU…VLHeixvR
11a946c454898d…7bd59304e1fce4
1 in β†’ 2 out16.1100 XPM192 B
AMBS7yS4…1vTatKpHAa3NPfF3…pqKaRrcw
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.

8.681 Γ— 10⁹⁴(95-digit number)
86817234557028302136…43644746670099203000
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
8.681 Γ— 10⁹⁴(95-digit number)
86817234557028302136…43644746670099202999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.681 Γ— 10⁹⁴(95-digit number)
86817234557028302136…43644746670099203001
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
1.736 Γ— 10⁹⁡(96-digit number)
17363446911405660427…87289493340198405999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.736 Γ— 10⁹⁡(96-digit number)
17363446911405660427…87289493340198406001
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
3.472 Γ— 10⁹⁡(96-digit number)
34726893822811320854…74578986680396811999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.472 Γ— 10⁹⁡(96-digit number)
34726893822811320854…74578986680396812001
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
6.945 Γ— 10⁹⁡(96-digit number)
69453787645622641709…49157973360793623999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.945 Γ— 10⁹⁡(96-digit number)
69453787645622641709…49157973360793624001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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 8
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 32519

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 a629fa7bfb89ce1afad877252b7d41321dc475de5a561106e6b4f41d90d8a9a0

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 #32,519 on Chainz β†—
Circulating Supply:57,758,542 XPMΒ·at block #6,814,309 Β· updates every 60s
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