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Home/Chain Registry/Block #2,833,415

Block #2,833,415

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/10/2018, 5:35:33 PM Β· Difficulty 11.7160 Β· 4,007,391 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b1f7f72d186d2c9d5e8238535fa229315cb9bc04c420d9772f9b6a8b9f201195
View on Chainz β†—

Difficulty

11.716023

Transactions

3

Size

847 B

Version

2

Bits

0bb74d45

Nonce

1,023,625,034

Timestamp

9/10/2018, 5:35:33 PM

Confirmations

4,007,391

Merkle Root

99c689a416bf9aca3d323e2072ea4277c68a409c037c6fc059b94f963b8e4b29
Transactions (3)
Coinbaseb99b23fc589415…29b9c7f322e1d0
1 in β†’ 1 out7.2900 XPM109 B
APdU3Xcv…ZpYKHg7o
f32e2acb4291c5…41851d7a0276d0
2 in β†’ 2 out14.5300 XPM307 B
AMANjgG3…fDX1sBurAKfN5ELc…A3YNDXZ8
c73526e42bcf16…d12a2bfd7d4258
2 in β†’ 2 out11.7900 XPM339 B
AW3QZZmg…j2rGjUkpAQS5qc4c…6ffKzMdV
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.

9.496 Γ— 10⁹⁸(99-digit number)
94968347495504993058…17163658413902725120
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
9.496 Γ— 10⁹⁸(99-digit number)
94968347495504993058…17163658413902725119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.496 Γ— 10⁹⁸(99-digit number)
94968347495504993058…17163658413902725121
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
1.899 Γ— 10⁹⁹(100-digit number)
18993669499100998611…34327316827805450239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.899 Γ— 10⁹⁹(100-digit number)
18993669499100998611…34327316827805450241
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
3.798 Γ— 10⁹⁹(100-digit number)
37987338998201997223…68654633655610900479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.798 Γ— 10⁹⁹(100-digit number)
37987338998201997223…68654633655610900481
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
7.597 Γ— 10⁹⁹(100-digit number)
75974677996403994446…37309267311221800959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.597 Γ— 10⁹⁹(100-digit number)
75974677996403994446…37309267311221800961
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
1.519 Γ— 10¹⁰⁰(101-digit number)
15194935599280798889…74618534622443601919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.519 Γ— 10¹⁰⁰(101-digit number)
15194935599280798889…74618534622443601921
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
3.038 Γ— 10¹⁰⁰(101-digit number)
30389871198561597778…49237069244887203839
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2833415

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 b1f7f72d186d2c9d5e8238535fa229315cb9bc04c420d9772f9b6a8b9f201195

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 #2,833,415 on Chainz β†—
Circulating Supply:57,970,797 XPMΒ·at block #6,840,805 Β· updates every 60s
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