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Home/Chain Registry/Block #2,939,783

Block #2,939,783

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/26/2018, 9:43:07 AM Β· Difficulty 11.3731 Β· 3,896,953 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
07fb016019e9645e360b81a46f1ff6388893aa818a8146fec88612371619a37b
View on Chainz β†—

Difficulty

11.373136

Transactions

1

Size

201 B

Version

2

Bits

0b5f85d9

Nonce

78,778,755

Timestamp

11/26/2018, 9:43:07 AM

Confirmations

3,896,953

Merkle Root

fb9d1468e60e193909aa540dd95d22e5f57e659c095e58aeb4316df9b6b5324b
Transactions (1)
Coinbasefb9d1468e60e19…316df9b6b5324b
1 in β†’ 1 out7.7200 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.

7.778 Γ— 10⁹⁢(97-digit number)
77783171105237079258…10843126292077911040
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
7.778 Γ— 10⁹⁢(97-digit number)
77783171105237079258…10843126292077911039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.778 Γ— 10⁹⁢(97-digit number)
77783171105237079258…10843126292077911041
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
1.555 Γ— 10⁹⁷(98-digit number)
15556634221047415851…21686252584155822079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.555 Γ— 10⁹⁷(98-digit number)
15556634221047415851…21686252584155822081
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
3.111 Γ— 10⁹⁷(98-digit number)
31113268442094831703…43372505168311644159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.111 Γ— 10⁹⁷(98-digit number)
31113268442094831703…43372505168311644161
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
6.222 Γ— 10⁹⁷(98-digit number)
62226536884189663407…86745010336623288319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.222 Γ— 10⁹⁷(98-digit number)
62226536884189663407…86745010336623288321
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
1.244 Γ— 10⁹⁸(99-digit number)
12445307376837932681…73490020673246576639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.244 Γ— 10⁹⁸(99-digit number)
12445307376837932681…73490020673246576641
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
2.489 Γ— 10⁹⁸(99-digit number)
24890614753675865362…46980041346493153279
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 2939783

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 07fb016019e9645e360b81a46f1ff6388893aa818a8146fec88612371619a37b

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 #2,939,783 on Chainz β†—
Circulating Supply:57,938,171 XPMΒ·at block #6,836,735 Β· updates every 60s
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