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Home/Chain Registry/Block #2,176,198

Block #2,176,198

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/24/2017, 9:29:48 PM Β· Difficulty 10.9187 Β· 4,665,848 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8605eef4ef56f47a57c357ddea910299abbdbee75ce9cbf7fef6865e1ec4a45c
View on Chainz β†—

Difficulty

10.918671

Transactions

2

Size

722 B

Version

2

Bits

0aeb2dfe

Nonce

995,535,628

Timestamp

6/24/2017, 9:29:48 PM

Confirmations

4,665,848

Merkle Root

a0b558b2ecfe79b43f5f596f1d521a8beb6637dd0156fe79afbdfc0ea2bf2efe
Transactions (2)
Coinbasef8c99326aebd3f…c6e80e0f15a4d5
1 in β†’ 1 out8.3900 XPM110 B
AURZwx39…v1izsce1
9c2698a6be0f41…712ec11aacfb6e
3 in β†’ 2 out1018.6157 XPM521 B
AZ7cQcwJ…NttCBkgLAXgkmXU6…MjhP8nmZ
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.

1.022 Γ— 10⁹⁢(97-digit number)
10226813810106489177…01576365286736276480
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
1.022 Γ— 10⁹⁢(97-digit number)
10226813810106489177…01576365286736276479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.022 Γ— 10⁹⁢(97-digit number)
10226813810106489177…01576365286736276481
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
2.045 Γ— 10⁹⁢(97-digit number)
20453627620212978354…03152730573472552959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.045 Γ— 10⁹⁢(97-digit number)
20453627620212978354…03152730573472552961
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
4.090 Γ— 10⁹⁢(97-digit number)
40907255240425956708…06305461146945105919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.090 Γ— 10⁹⁢(97-digit number)
40907255240425956708…06305461146945105921
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
8.181 Γ— 10⁹⁢(97-digit number)
81814510480851913416…12610922293890211839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.181 Γ— 10⁹⁢(97-digit number)
81814510480851913416…12610922293890211841
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
1.636 Γ— 10⁹⁷(98-digit number)
16362902096170382683…25221844587780423679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.636 Γ— 10⁹⁷(98-digit number)
16362902096170382683…25221844587780423681
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 2176198

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 8605eef4ef56f47a57c357ddea910299abbdbee75ce9cbf7fef6865e1ec4a45c

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 #2,176,198 on Chainz β†—
Circulating Supply:57,980,749 XPMΒ·at block #6,842,045 Β· updates every 60s
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