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Block #2,257,250

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/18/2017, 12:40:56 PM Β· Difficulty 10.9516 Β· 4,587,593 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fa546eced4ee7151709ae769eae3bd99310d52ce4a0454c10b7dcb65e7e3d933
View on Chainz β†—

Difficulty

10.951572

Transactions

2

Size

426 B

Version

2

Bits

0af39a34

Nonce

2,035,196,459

Timestamp

8/18/2017, 12:40:56 PM

Confirmations

4,587,593

Merkle Root

2dcce8581e70df4be633c06a4650a37b95673ff64a02f0aa91731ae4b31c9175
Transactions (2)
Coinbase76d66064a29720…56a8a82caf1cad
1 in β†’ 1 out8.3300 XPM110 B
ATtrSpnJ…wyQL6Afd
3ca2b5d3938c1f…639dc8a09e067a
1 in β†’ 2 out9564.6073 XPM226 B
AUn2Kwfi…R8KZwnsuAM3BXNZd…KY5iHqro
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.

8.824 Γ— 10⁹⁴(95-digit number)
88242056826197810228…04061835550778154880
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
8.824 Γ— 10⁹⁴(95-digit number)
88242056826197810228…04061835550778154879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.824 Γ— 10⁹⁴(95-digit number)
88242056826197810228…04061835550778154881
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
1.764 Γ— 10⁹⁡(96-digit number)
17648411365239562045…08123671101556309759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.764 Γ— 10⁹⁡(96-digit number)
17648411365239562045…08123671101556309761
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
3.529 Γ— 10⁹⁡(96-digit number)
35296822730479124091…16247342203112619519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.529 Γ— 10⁹⁡(96-digit number)
35296822730479124091…16247342203112619521
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
7.059 Γ— 10⁹⁡(96-digit number)
70593645460958248182…32494684406225239039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.059 Γ— 10⁹⁡(96-digit number)
70593645460958248182…32494684406225239041
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
1.411 Γ— 10⁹⁢(97-digit number)
14118729092191649636…64989368812450478079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.411 Γ— 10⁹⁢(97-digit number)
14118729092191649636…64989368812450478081
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
2.823 Γ— 10⁹⁢(97-digit number)
28237458184383299273…29978737624900956159
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 2257250

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 fa546eced4ee7151709ae769eae3bd99310d52ce4a0454c10b7dcb65e7e3d933

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 #2,257,250 on Chainz β†—
Circulating Supply:58,003,153 XPMΒ·at block #6,844,842 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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