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Home/Chain Registry/Block #2,635,594

Block #2,635,594

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 4/29/2018, 7:20:24 AM Β· Difficulty 11.3266 Β· 4,202,401 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0b3e2bf13a0bc99df3fb0114f4c66f40ea57d68a6457d0a84f6f1d248d481966
View on Chainz β†—

Difficulty

11.326614

Transactions

1

Size

202 B

Version

2

Bits

0b539cf6

Nonce

490,347,832

Timestamp

4/29/2018, 7:20:24 AM

Confirmations

4,202,401

Merkle Root

9b868cfa11026c4079a5d8d73d3653b8c1b49e4d04023cb77f1e8bf564e47335
Transactions (1)
Coinbase9b868cfa11026c…1e8bf564e47335
1 in β†’ 1 out7.7800 XPM110 B
Adqah8zh…1WwoHJ9t
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.

5.613 Γ— 10⁹⁸(99-digit number)
56135930977980689332…41331317616136028160
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
5.613 Γ— 10⁹⁸(99-digit number)
56135930977980689332…41331317616136028159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.613 Γ— 10⁹⁸(99-digit number)
56135930977980689332…41331317616136028161
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
1.122 Γ— 10⁹⁹(100-digit number)
11227186195596137866…82662635232272056319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.122 Γ— 10⁹⁹(100-digit number)
11227186195596137866…82662635232272056321
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
2.245 Γ— 10⁹⁹(100-digit number)
22454372391192275732…65325270464544112639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.245 Γ— 10⁹⁹(100-digit number)
22454372391192275732…65325270464544112641
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
4.490 Γ— 10⁹⁹(100-digit number)
44908744782384551465…30650540929088225279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.490 Γ— 10⁹⁹(100-digit number)
44908744782384551465…30650540929088225281
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
8.981 Γ— 10⁹⁹(100-digit number)
89817489564769102931…61301081858176450559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.981 Γ— 10⁹⁹(100-digit number)
89817489564769102931…61301081858176450561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.796 Γ— 10¹⁰⁰(101-digit number)
17963497912953820586…22602163716352901119
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
1.796 Γ— 10¹⁰⁰(101-digit number)
17963497912953820586…22602163716352901121
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2635594

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 0b3e2bf13a0bc99df3fb0114f4c66f40ea57d68a6457d0a84f6f1d248d481966

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 #2,635,594 on Chainz β†—
Circulating Supply:57,948,311 XPMΒ·at block #6,837,994 Β· updates every 60s
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