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Block #89,054

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/30/2013, 2:24:36 AM Β· Difficulty 9.2603 Β· 6,710,849 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c811ce6176d684fd8aadde77df37f8f110d3e96ce7ad58ae6f5c62f66f9f5731
View on Chainz β†—

Height

#89,054

Difficulty

9.260277

Transactions

1

Size

201 B

Version

2

Bits

0942a17c

Nonce

314,923

Timestamp

7/30/2013, 2:24:36 AM

Confirmations

6,710,849

Merkle Root

33a6d0d92b09af91fb4b39d8ca45ad5bb6c813506e6eb61720af7d6c25bc26cd
Transactions (1)
Coinbase33a6d0d92b09af…af7d6c25bc26cd
1 in β†’ 1 out11.6400 XPM110 B
AXJvhFyz…zFNFhzY8
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.

1.083 Γ— 10⁹⁸(99-digit number)
10833091589509018437…75598697202048031600
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
1.083 Γ— 10⁹⁸(99-digit number)
10833091589509018437…75598697202048031599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.083 Γ— 10⁹⁸(99-digit number)
10833091589509018437…75598697202048031601
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
2.166 Γ— 10⁹⁸(99-digit number)
21666183179018036874…51197394404096063199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.166 Γ— 10⁹⁸(99-digit number)
21666183179018036874…51197394404096063201
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
4.333 Γ— 10⁹⁸(99-digit number)
43332366358036073749…02394788808192126399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.333 Γ— 10⁹⁸(99-digit number)
43332366358036073749…02394788808192126401
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
8.666 Γ— 10⁹⁸(99-digit number)
86664732716072147499…04789577616384252799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.666 Γ— 10⁹⁸(99-digit number)
86664732716072147499…04789577616384252801
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
1.733 Γ— 10⁹⁹(100-digit number)
17332946543214429499…09579155232768505599
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 89054

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 c811ce6176d684fd8aadde77df37f8f110d3e96ce7ad58ae6f5c62f66f9f5731

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 #89,054 on Chainz β†—
Circulating Supply:57,643,279 XPMΒ·at block #6,799,902 Β· updates every 60s
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