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Home/Chain Registry/Block #2,233,767

Block #2,233,767

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/2/2017, 1:07:48 PM Β· Difficulty 10.9461 Β· 4,596,769 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
15e24702f7e152d342eb455b0818455b6bdbec800f0ee2903cf1719ea6a5cdc9
View on Chainz β†—

Difficulty

10.946107

Transactions

2

Size

576 B

Version

2

Bits

0af23418

Nonce

506,274,682

Timestamp

8/2/2017, 1:07:48 PM

Confirmations

4,596,769

Merkle Root

4f4f5809e458fcef8cf1ddcf06c049ae5604583cb085d644ef1d3222425281b8
Transactions (2)
Coinbasea88609e860fa49…c5cbea0f44921b
1 in β†’ 1 out8.3400 XPM110 B
AUuGSicR…o6JTLVmz
efaeb1d5ed1c77…fb211dabb36527
2 in β†’ 2 out417.7502 XPM375 B
AaxZhJKy…kKzk69YRAPwc1FGE…M3B3W9Bf
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.

2.727 Γ— 10⁹⁢(97-digit number)
27278073356316739711…45557919609686036480
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
2.727 Γ— 10⁹⁢(97-digit number)
27278073356316739711…45557919609686036479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.727 Γ— 10⁹⁢(97-digit number)
27278073356316739711…45557919609686036481
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
5.455 Γ— 10⁹⁢(97-digit number)
54556146712633479423…91115839219372072959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.455 Γ— 10⁹⁢(97-digit number)
54556146712633479423…91115839219372072961
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
1.091 Γ— 10⁹⁷(98-digit number)
10911229342526695884…82231678438744145919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.091 Γ— 10⁹⁷(98-digit number)
10911229342526695884…82231678438744145921
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
2.182 Γ— 10⁹⁷(98-digit number)
21822458685053391769…64463356877488291839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.182 Γ— 10⁹⁷(98-digit number)
21822458685053391769…64463356877488291841
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
4.364 Γ— 10⁹⁷(98-digit number)
43644917370106783538…28926713754976583679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.364 Γ— 10⁹⁷(98-digit number)
43644917370106783538…28926713754976583681
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
8.728 Γ— 10⁹⁷(98-digit number)
87289834740213567076…57853427509953167359
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 2233767

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 15e24702f7e152d342eb455b0818455b6bdbec800f0ee2903cf1719ea6a5cdc9

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 #2,233,767 on Chainz β†—
Circulating Supply:57,888,535 XPMΒ·at block #6,830,535 Β· updates every 60s
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