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Home/Chain Registry/Block #1,736,253

Block #1,736,253

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/27/2016, 9:57:01 AM Β· Difficulty 10.7181 Β· 5,107,054 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
49996a6da52c00c2dfb16fad75a37d777bf08ec7d202fefc523960477149f341
View on Chainz β†—

Difficulty

10.718080

Transactions

1

Size

201 B

Version

2

Bits

0ab7d412

Nonce

1,409,186,588

Timestamp

8/27/2016, 9:57:01 AM

Confirmations

5,107,054

Merkle Root

238a3e6a5586a527d8feb0216f893c6f371610aeb1eedf03c12e58a399dd7765
Transactions (1)
Coinbase238a3e6a5586a5…2e58a399dd7765
1 in β†’ 1 out8.6900 XPM110 B
AXqg59rV…wqMkpuX6
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.

1.878 Γ— 10⁹⁸(99-digit number)
18784835509507689664…62113433261519175680
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
1.878 Γ— 10⁹⁸(99-digit number)
18784835509507689664…62113433261519175679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.878 Γ— 10⁹⁸(99-digit number)
18784835509507689664…62113433261519175681
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
3.756 Γ— 10⁹⁸(99-digit number)
37569671019015379329…24226866523038351359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.756 Γ— 10⁹⁸(99-digit number)
37569671019015379329…24226866523038351361
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
7.513 Γ— 10⁹⁸(99-digit number)
75139342038030758659…48453733046076702719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.513 Γ— 10⁹⁸(99-digit number)
75139342038030758659…48453733046076702721
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
1.502 Γ— 10⁹⁹(100-digit number)
15027868407606151731…96907466092153405439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.502 Γ— 10⁹⁹(100-digit number)
15027868407606151731…96907466092153405441
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
3.005 Γ— 10⁹⁹(100-digit number)
30055736815212303463…93814932184306810879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.005 Γ— 10⁹⁹(100-digit number)
30055736815212303463…93814932184306810881
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 1736253

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 49996a6da52c00c2dfb16fad75a37d777bf08ec7d202fefc523960477149f341

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 #1,736,253 on Chainz β†—
Circulating Supply:57,990,822 XPMΒ·at block #6,843,306 Β· updates every 60s
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