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Home/Chain Registry/Block #1,960,824

Block #1,960,824

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/30/2017, 4:07:05 AM Β· Difficulty 10.7422 Β· 4,870,872 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7c3f457d7f41982420314587c3848edfb324a88dc0f4291866b8e923ce7b7424
View on Chainz β†—

Difficulty

10.742243

Transactions

1

Size

201 B

Version

2

Bits

0abe03a8

Nonce

433,465,108

Timestamp

1/30/2017, 4:07:05 AM

Confirmations

4,870,872

Merkle Root

d30c21d4301f45e6b4fcdf042c90db9267806ba19ab57c2d2b96e8a638bf4511
Transactions (1)
Coinbased30c21d4301f45…96e8a638bf4511
1 in β†’ 1 out8.6500 XPM110 B
AJvvapk2…EZvp2wbX
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.

4.435 Γ— 10⁹⁷(98-digit number)
44357574601778342995…65317515603269632000
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
4.435 Γ— 10⁹⁷(98-digit number)
44357574601778342995…65317515603269631999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.435 Γ— 10⁹⁷(98-digit number)
44357574601778342995…65317515603269632001
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
8.871 Γ— 10⁹⁷(98-digit number)
88715149203556685990…30635031206539263999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.871 Γ— 10⁹⁷(98-digit number)
88715149203556685990…30635031206539264001
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
1.774 Γ— 10⁹⁸(99-digit number)
17743029840711337198…61270062413078527999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.774 Γ— 10⁹⁸(99-digit number)
17743029840711337198…61270062413078528001
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
3.548 Γ— 10⁹⁸(99-digit number)
35486059681422674396…22540124826157055999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.548 Γ— 10⁹⁸(99-digit number)
35486059681422674396…22540124826157056001
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
7.097 Γ— 10⁹⁸(99-digit number)
70972119362845348792…45080249652314111999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.097 Γ— 10⁹⁸(99-digit number)
70972119362845348792…45080249652314112001
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 1960824

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 7c3f457d7f41982420314587c3848edfb324a88dc0f4291866b8e923ce7b7424

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 #1,960,824 on Chainz β†—
Circulating Supply:57,897,677 XPMΒ·at block #6,831,695 Β· updates every 60s
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