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Home/Chain Registry/Block #3,058,880

Block #3,058,880

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/18/2019, 10:43:05 PM Β· Difficulty 11.0100 Β· 3,782,572 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
33d8450a53ac956dd2abe81d243f41501691f2b8b8d0d110590980475a68afc3
View on Chainz β†—

Difficulty

11.010023

Transactions

1

Size

200 B

Version

2

Bits

0b0290e1

Nonce

1,197,273,630

Timestamp

2/18/2019, 10:43:05 PM

Confirmations

3,782,572

Merkle Root

cfd12de34f21d2b001d0f30e15ec0787d266cadf20a3479ff3daa6194b31a813
Transactions (1)
Coinbasecfd12de34f21d2…daa6194b31a813
1 in β†’ 1 out8.2400 XPM110 B
AUMQRepm…tAfKmdW1
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.

2.503 Γ— 10⁹⁡(96-digit number)
25033437817584675120…26953677717225111040
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
2.503 Γ— 10⁹⁡(96-digit number)
25033437817584675120…26953677717225111039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.503 Γ— 10⁹⁡(96-digit number)
25033437817584675120…26953677717225111041
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
5.006 Γ— 10⁹⁡(96-digit number)
50066875635169350240…53907355434450222079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.006 Γ— 10⁹⁡(96-digit number)
50066875635169350240…53907355434450222081
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
1.001 Γ— 10⁹⁢(97-digit number)
10013375127033870048…07814710868900444159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.001 Γ— 10⁹⁢(97-digit number)
10013375127033870048…07814710868900444161
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
2.002 Γ— 10⁹⁢(97-digit number)
20026750254067740096…15629421737800888319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.002 Γ— 10⁹⁢(97-digit number)
20026750254067740096…15629421737800888321
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
4.005 Γ— 10⁹⁢(97-digit number)
40053500508135480192…31258843475601776639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.005 Γ— 10⁹⁢(97-digit number)
40053500508135480192…31258843475601776641
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
8.010 Γ— 10⁹⁢(97-digit number)
80107001016270960384…62517686951203553279
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 3058880

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 33d8450a53ac956dd2abe81d243f41501691f2b8b8d0d110590980475a68afc3

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 #3,058,880 on Chainz β†—
Circulating Supply:57,975,996 XPMΒ·at block #6,841,451 Β· updates every 60s
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