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Home/Chain Registry/Block #2,813,002

Block #2,813,002

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/28/2018, 12:23:19 AM Β· Difficulty 11.6753 Β· 4,032,709 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3a66e8cc431a77587ec26ba759172aa7f3720a52a40b3cdb1c875bad1c37944c
View on Chainz β†—

Difficulty

11.675323

Transactions

1

Size

202 B

Version

2

Bits

0bace1f5

Nonce

2,074,142,489

Timestamp

8/28/2018, 12:23:19 AM

Confirmations

4,032,709

Merkle Root

572990a5a1de6f959b480256f67861a7ed4f6cf4c1bfeb6c1898128f791c525a
Transactions (1)
Coinbase572990a5a1de6f…98128f791c525a
1 in β†’ 1 out7.3200 XPM110 B
AGcUBwda…du6222EQ
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.

6.043 Γ— 10⁹⁸(99-digit number)
60434594622944990863…69790129932190351360
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
6.043 Γ— 10⁹⁸(99-digit number)
60434594622944990863…69790129932190351359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.043 Γ— 10⁹⁸(99-digit number)
60434594622944990863…69790129932190351361
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
1.208 Γ— 10⁹⁹(100-digit number)
12086918924588998172…39580259864380702719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.208 Γ— 10⁹⁹(100-digit number)
12086918924588998172…39580259864380702721
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
2.417 Γ— 10⁹⁹(100-digit number)
24173837849177996345…79160519728761405439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.417 Γ— 10⁹⁹(100-digit number)
24173837849177996345…79160519728761405441
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
4.834 Γ— 10⁹⁹(100-digit number)
48347675698355992690…58321039457522810879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.834 Γ— 10⁹⁹(100-digit number)
48347675698355992690…58321039457522810881
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
9.669 Γ— 10⁹⁹(100-digit number)
96695351396711985381…16642078915045621759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.669 Γ— 10⁹⁹(100-digit number)
96695351396711985381…16642078915045621761
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
1.933 Γ— 10¹⁰⁰(101-digit number)
19339070279342397076…33284157830091243519
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 2813002

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 3a66e8cc431a77587ec26ba759172aa7f3720a52a40b3cdb1c875bad1c37944c

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 #2,813,002 on Chainz β†—
Circulating Supply:58,010,147 XPMΒ·at block #6,845,710 Β· updates every 60s
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