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Home/Chain Registry/Block #2,036,131

Block #2,036,131

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/24/2017, 6:42:15 AM Β· Difficulty 10.6791 Β· 4,807,170 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
16eb6dd73b5e32d2a38d6058a4c5f7d549efe0dca18bb4c0a0d9246b2f8415ff
View on Chainz β†—

Difficulty

10.679134

Transactions

1

Size

199 B

Version

2

Bits

0aaddbba

Nonce

406,391,440

Timestamp

3/24/2017, 6:42:15 AM

Confirmations

4,807,170

Merkle Root

e0fee1c446dbbfc1315c14f40d9ea4abceefa05db8b71d1a2fadd64d490705e2
Transactions (1)
Coinbasee0fee1c446dbbf…add64d490705e2
1 in β†’ 1 out8.7500 XPM109 B
AHo9cmcD…mKaos3gD
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.

1.794 Γ— 10⁹⁡(96-digit number)
17945730597321235087…06733218584576301120
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
1.794 Γ— 10⁹⁡(96-digit number)
17945730597321235087…06733218584576301119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.794 Γ— 10⁹⁡(96-digit number)
17945730597321235087…06733218584576301121
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
3.589 Γ— 10⁹⁡(96-digit number)
35891461194642470174…13466437169152602239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.589 Γ— 10⁹⁡(96-digit number)
35891461194642470174…13466437169152602241
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
7.178 Γ— 10⁹⁡(96-digit number)
71782922389284940348…26932874338305204479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.178 Γ— 10⁹⁡(96-digit number)
71782922389284940348…26932874338305204481
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
1.435 Γ— 10⁹⁢(97-digit number)
14356584477856988069…53865748676610408959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.435 Γ— 10⁹⁢(97-digit number)
14356584477856988069…53865748676610408961
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
2.871 Γ— 10⁹⁢(97-digit number)
28713168955713976139…07731497353220817919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.871 Γ— 10⁹⁢(97-digit number)
28713168955713976139…07731497353220817921
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
5.742 Γ— 10⁹⁢(97-digit number)
57426337911427952279…15462994706441635839
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 2036131

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 16eb6dd73b5e32d2a38d6058a4c5f7d549efe0dca18bb4c0a0d9246b2f8415ff

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 #2,036,131 on Chainz β†—
Circulating Supply:57,990,773 XPMΒ·at block #6,843,300 Β· updates every 60s
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