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Block #32,882

TWNLength 7β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 3:44:33 AM Β· Difficulty 7.9911 Β· 6,784,386 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ed0f1e7f2f43e01fcfbe0f3d71c4970fde26aad7f67e7201ef61991278d7a0d9
View on Chainz β†—

Height

#32,882

Difficulty

7.991098

Transactions

1

Size

198 B

Version

2

Bits

07fdb89f

Nonce

42

Timestamp

7/14/2013, 3:44:33 AM

Confirmations

6,784,386

Merkle Root

0aa108f37ae6e0f268263e2a09595144158f445666946e6f493c6564ea4fce15
Transactions (1)
Coinbase0aa108f37ae6e0…3c6564ea4fce15
1 in β†’ 1 out15.6400 XPM109 B
ASbRxSSz…H5rkdjdH
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.

1.957 Γ— 10⁹³(94-digit number)
19578232296601080250…55704485663771384000
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
1.957 Γ— 10⁹³(94-digit number)
19578232296601080250…55704485663771383999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.957 Γ— 10⁹³(94-digit number)
19578232296601080250…55704485663771384001
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
3.915 Γ— 10⁹³(94-digit number)
39156464593202160501…11408971327542767999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.915 Γ— 10⁹³(94-digit number)
39156464593202160501…11408971327542768001
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
7.831 Γ— 10⁹³(94-digit number)
78312929186404321002…22817942655085535999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.831 Γ— 10⁹³(94-digit number)
78312929186404321002…22817942655085536001
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
1.566 Γ— 10⁹⁴(95-digit number)
15662585837280864200…45635885310171071999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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 7
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 32882

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 ed0f1e7f2f43e01fcfbe0f3d71c4970fde26aad7f67e7201ef61991278d7a0d9

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 #32,882 on Chainz β†—
Circulating Supply:57,782,181 XPMΒ·at block #6,817,267 Β· updates every 60s
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