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Home/Chain Registry/Block #2,131,690

Block #2,131,690

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/25/2017, 6:47:53 AM Β· Difficulty 10.9103 Β· 4,694,429 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4ad3d18247eafbfa91935199dc0273076855e6498131fb7ee8f77a0ae93212f7
View on Chainz β†—

Difficulty

10.910263

Transactions

1

Size

200 B

Version

2

Bits

0ae906fc

Nonce

351,627,277

Timestamp

5/25/2017, 6:47:53 AM

Confirmations

4,694,429

Merkle Root

d2a8dbb507720a938de72df04f84f27e2b76b6c118b8b9e220716d486975836d
Transactions (1)
Coinbased2a8dbb507720a…716d486975836d
1 in β†’ 1 out8.3900 XPM109 B
AbJCpYmt…nmG9ybNg
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.

3.124 Γ— 10⁹⁢(97-digit number)
31240658035368623341…70166353856395345920
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
3.124 Γ— 10⁹⁢(97-digit number)
31240658035368623341…70166353856395345919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.124 Γ— 10⁹⁢(97-digit number)
31240658035368623341…70166353856395345921
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
6.248 Γ— 10⁹⁢(97-digit number)
62481316070737246683…40332707712790691839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.248 Γ— 10⁹⁢(97-digit number)
62481316070737246683…40332707712790691841
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
1.249 Γ— 10⁹⁷(98-digit number)
12496263214147449336…80665415425581383679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.249 Γ— 10⁹⁷(98-digit number)
12496263214147449336…80665415425581383681
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
2.499 Γ— 10⁹⁷(98-digit number)
24992526428294898673…61330830851162767359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.499 Γ— 10⁹⁷(98-digit number)
24992526428294898673…61330830851162767361
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
4.998 Γ— 10⁹⁷(98-digit number)
49985052856589797347…22661661702325534719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.998 Γ— 10⁹⁷(98-digit number)
49985052856589797347…22661661702325534721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2131690

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 4ad3d18247eafbfa91935199dc0273076855e6498131fb7ee8f77a0ae93212f7

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 #2,131,690 on Chainz β†—
Circulating Supply:57,853,077 XPMΒ·at block #6,826,118 Β· updates every 60s
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