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Block #81,988

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/25/2013, 3:27:28 AM Β· Difficulty 9.2702 Β· 6,730,863 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
22d2ccdaa758c9e9455f5c6ab2f6fde79b00b902b1a73e5c2c40d4891dc95546
View on Chainz β†—

Height

#81,988

Difficulty

9.270214

Transactions

2

Size

688 B

Version

2

Bits

09452cc6

Nonce

94,220

Timestamp

7/25/2013, 3:27:28 AM

Confirmations

6,730,863

Merkle Root

4368717ff704d30ed179232e50a9dcb0a63021ef8cef62f43317a657caa29073
Transactions (2)
Coinbase442932dc759d23…53c0c1d8c88ba4
1 in β†’ 1 out11.6300 XPM109 B
AP8LPysx…ki6cuukz
599b2a86df0fa8…ef00ff1f409b97
3 in β†’ 1 out46.8700 XPM489 B
AJv5WoqT…tqCRQqFk
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.

1.766 Γ— 10⁹⁡(96-digit number)
17668322918111397294…05149205557797425000
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
1.766 Γ— 10⁹⁡(96-digit number)
17668322918111397294…05149205557797424999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.766 Γ— 10⁹⁡(96-digit number)
17668322918111397294…05149205557797425001
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
3.533 Γ— 10⁹⁡(96-digit number)
35336645836222794589…10298411115594849999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.533 Γ— 10⁹⁡(96-digit number)
35336645836222794589…10298411115594850001
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
7.067 Γ— 10⁹⁡(96-digit number)
70673291672445589178…20596822231189699999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.067 Γ— 10⁹⁡(96-digit number)
70673291672445589178…20596822231189700001
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
1.413 Γ— 10⁹⁢(97-digit number)
14134658334489117835…41193644462379399999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.413 Γ— 10⁹⁢(97-digit number)
14134658334489117835…41193644462379400001
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
2.826 Γ— 10⁹⁢(97-digit number)
28269316668978235671…82387288924758799999
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 81988

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 22d2ccdaa758c9e9455f5c6ab2f6fde79b00b902b1a73e5c2c40d4891dc95546

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 #81,988 on Chainz β†—
Circulating Supply:57,746,843 XPMΒ·at block #6,812,850 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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