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Home/Chain Registry/Block #2,727,163

Block #2,727,163

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/29/2018, 8:36:19 PM Β· Difficulty 11.6272 Β· 4,117,707 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
710f8ed39d6e3d389c8ecc61c3a2e8df27a96420a8d1b8ad1a054f1f43302e23
View on Chainz β†—

Difficulty

11.627244

Transactions

1

Size

201 B

Version

2

Bits

0ba09317

Nonce

2,134,901,812

Timestamp

6/29/2018, 8:36:19 PM

Confirmations

4,117,707

Merkle Root

85b0e4b4d0bb8b18cb8cb9e4baf11279fb3660f46ea288d2c9fef47dac34b144
Transactions (1)
Coinbase85b0e4b4d0bb8b…fef47dac34b144
1 in β†’ 1 out7.3800 XPM110 B
AepMuXxR…o8PPdKc2
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.

1.013 Γ— 10⁹⁢(97-digit number)
10135950590331273543…56116235495662983040
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
1.013 Γ— 10⁹⁢(97-digit number)
10135950590331273543…56116235495662983039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.013 Γ— 10⁹⁢(97-digit number)
10135950590331273543…56116235495662983041
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
2.027 Γ— 10⁹⁢(97-digit number)
20271901180662547086…12232470991325966079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.027 Γ— 10⁹⁢(97-digit number)
20271901180662547086…12232470991325966081
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
4.054 Γ— 10⁹⁢(97-digit number)
40543802361325094173…24464941982651932159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.054 Γ— 10⁹⁢(97-digit number)
40543802361325094173…24464941982651932161
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
8.108 Γ— 10⁹⁢(97-digit number)
81087604722650188346…48929883965303864319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.108 Γ— 10⁹⁢(97-digit number)
81087604722650188346…48929883965303864321
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
1.621 Γ— 10⁹⁷(98-digit number)
16217520944530037669…97859767930607728639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.621 Γ— 10⁹⁷(98-digit number)
16217520944530037669…97859767930607728641
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
3.243 Γ— 10⁹⁷(98-digit number)
32435041889060075338…95719535861215457279
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 2727163

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 710f8ed39d6e3d389c8ecc61c3a2e8df27a96420a8d1b8ad1a054f1f43302e23

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 #2,727,163 on Chainz β†—
Circulating Supply:58,003,372 XPMΒ·at block #6,844,869 Β· updates every 60s
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