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Home/Chain Registry/Block #2,049,416

Block #2,049,416

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/2/2017, 8:38:11 AM Β· Difficulty 10.6942 Β· 4,793,274 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
00a5b2788830a9feef5f4bd8ea8614ac9ce30e3abb465f8c53f849da2f201548
View on Chainz β†—

Difficulty

10.694230

Transactions

1

Size

199 B

Version

2

Bits

0ab1b915

Nonce

547,186,917

Timestamp

4/2/2017, 8:38:11 AM

Confirmations

4,793,274

Merkle Root

03a806e8d56c23e32b3c99121c6c1f6749e4751c1c8f6b217282346a018a0309
Transactions (1)
Coinbase03a806e8d56c23…82346a018a0309
1 in β†’ 1 out8.7300 XPM109 B
AQiuSpxv…hrBT1kJg
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.

2.363 Γ— 10⁹⁴(95-digit number)
23638860297959733753…74970896340314390780
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
2.363 Γ— 10⁹⁴(95-digit number)
23638860297959733753…74970896340314390779
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.363 Γ— 10⁹⁴(95-digit number)
23638860297959733753…74970896340314390781
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
4.727 Γ— 10⁹⁴(95-digit number)
47277720595919467507…49941792680628781559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.727 Γ— 10⁹⁴(95-digit number)
47277720595919467507…49941792680628781561
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
9.455 Γ— 10⁹⁴(95-digit number)
94555441191838935014…99883585361257563119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.455 Γ— 10⁹⁴(95-digit number)
94555441191838935014…99883585361257563121
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
1.891 Γ— 10⁹⁡(96-digit number)
18911088238367787002…99767170722515126239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.891 Γ— 10⁹⁡(96-digit number)
18911088238367787002…99767170722515126241
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
3.782 Γ— 10⁹⁡(96-digit number)
37822176476735574005…99534341445030252479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.782 Γ— 10⁹⁡(96-digit number)
37822176476735574005…99534341445030252481
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
7.564 Γ— 10⁹⁡(96-digit number)
75644352953471148011…99068682890060504959
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 2049416

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 00a5b2788830a9feef5f4bd8ea8614ac9ce30e3abb465f8c53f849da2f201548

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 #2,049,416 on Chainz β†—
Circulating Supply:57,985,867 XPMΒ·at block #6,842,689 Β· updates every 60s
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