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Block #2,816,515

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/30/2018, 7:42:53 AM Β· Difficulty 11.6877 Β· 4,009,926 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
94989f8f0fe9e799a2cd497cb8d018f6f52434f29d0deee1ca2aaf9a2a3f6d4d
View on Chainz β†—

Difficulty

11.687696

Transactions

1

Size

201 B

Version

2

Bits

0bb00ce0

Nonce

1,437,329,570

Timestamp

8/30/2018, 7:42:53 AM

Confirmations

4,009,926

Merkle Root

8a69ae668921cfe9ff069dd49f20d0076391a7573ee31ecd2ad22c610569a93c
Transactions (1)
Coinbase8a69ae668921cf…d22c610569a93c
1 in β†’ 1 out7.3100 XPM109 B
ANAdrDTX…PeDqDUKV
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.

3.369 Γ— 10⁹⁸(99-digit number)
33692309914705651118…10903265263152660480
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
3.369 Γ— 10⁹⁸(99-digit number)
33692309914705651118…10903265263152660479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.369 Γ— 10⁹⁸(99-digit number)
33692309914705651118…10903265263152660481
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
6.738 Γ— 10⁹⁸(99-digit number)
67384619829411302237…21806530526305320959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.738 Γ— 10⁹⁸(99-digit number)
67384619829411302237…21806530526305320961
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
1.347 Γ— 10⁹⁹(100-digit number)
13476923965882260447…43613061052610641919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.347 Γ— 10⁹⁹(100-digit number)
13476923965882260447…43613061052610641921
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
2.695 Γ— 10⁹⁹(100-digit number)
26953847931764520895…87226122105221283839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.695 Γ— 10⁹⁹(100-digit number)
26953847931764520895…87226122105221283841
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
5.390 Γ— 10⁹⁹(100-digit number)
53907695863529041790…74452244210442567679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.390 Γ— 10⁹⁹(100-digit number)
53907695863529041790…74452244210442567681
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
1.078 Γ— 10¹⁰⁰(101-digit number)
10781539172705808358…48904488420885135359
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 2816515

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 94989f8f0fe9e799a2cd497cb8d018f6f52434f29d0deee1ca2aaf9a2a3f6d4d

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 #2,816,515 on Chainz β†—
Circulating Supply:57,855,664 XPMΒ·at block #6,826,440 Β· updates every 60s
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