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Home/Chain Registry/Block #3,065,654

Block #3,065,654

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/23/2019, 6:56:26 PM Β· Difficulty 10.9960 Β· 3,776,334 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
29037fe88e012705ea74b2335195952ff7281a3c6756140931d1faae366ebd15
View on Chainz β†—

Difficulty

10.996045

Transactions

1

Size

200 B

Version

2

Bits

0afefcd4

Nonce

243,654,402

Timestamp

2/23/2019, 6:56:26 PM

Confirmations

3,776,334

Merkle Root

f9c2904600e91c96862383b9518f0fa1bc6b00f5fe506197fb84dacd1ebfd5d6
Transactions (1)
Coinbasef9c2904600e91c…84dacd1ebfd5d6
1 in β†’ 1 out8.2600 XPM110 B
AbXwmGxD…4XXYP765
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.

2.365 Γ— 10⁹⁴(95-digit number)
23654766366504135480…45454488955855052800
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
2.365 Γ— 10⁹⁴(95-digit number)
23654766366504135480…45454488955855052799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.365 Γ— 10⁹⁴(95-digit number)
23654766366504135480…45454488955855052801
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
4.730 Γ— 10⁹⁴(95-digit number)
47309532733008270961…90908977911710105599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.730 Γ— 10⁹⁴(95-digit number)
47309532733008270961…90908977911710105601
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
9.461 Γ— 10⁹⁴(95-digit number)
94619065466016541922…81817955823420211199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.461 Γ— 10⁹⁴(95-digit number)
94619065466016541922…81817955823420211201
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
1.892 Γ— 10⁹⁡(96-digit number)
18923813093203308384…63635911646840422399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.892 Γ— 10⁹⁡(96-digit number)
18923813093203308384…63635911646840422401
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
3.784 Γ— 10⁹⁡(96-digit number)
37847626186406616768…27271823293680844799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.784 Γ— 10⁹⁡(96-digit number)
37847626186406616768…27271823293680844801
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
7.569 Γ— 10⁹⁡(96-digit number)
75695252372813233537…54543646587361689599
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 3065654

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 29037fe88e012705ea74b2335195952ff7281a3c6756140931d1faae366ebd15

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 #3,065,654 on Chainz β†—
Circulating Supply:57,980,290 XPMΒ·at block #6,841,987 Β· updates every 60s
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