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Home/Chain Registry/Block #2,996,263

Block #2,996,263

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/5/2019, 5:07:05 AM Β· Difficulty 11.2615 Β· 3,835,145 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
52152a6c4aa1777a13024f6163196fa20fcd45ac0ba25c134a9a2227a05da0dd
View on Chainz β†—

Difficulty

11.261465

Transactions

1

Size

201 B

Version

2

Bits

0b42ef60

Nonce

455,961,098

Timestamp

1/5/2019, 5:07:05 AM

Confirmations

3,835,145

Merkle Root

307729e014be07b9849002460f272c78bf0935fb9a50e1828286565200a631ac
Transactions (1)
Coinbase307729e014be07…86565200a631ac
1 in β†’ 1 out7.8700 XPM109 B
AUhjokok…k5m93PZR
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.

2.474 Γ— 10⁹⁹(100-digit number)
24749839967434467891…53676584467522519040
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
2.474 Γ— 10⁹⁹(100-digit number)
24749839967434467891…53676584467522519039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.474 Γ— 10⁹⁹(100-digit number)
24749839967434467891…53676584467522519041
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
4.949 Γ— 10⁹⁹(100-digit number)
49499679934868935782…07353168935045038079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.949 Γ— 10⁹⁹(100-digit number)
49499679934868935782…07353168935045038081
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
9.899 Γ— 10⁹⁹(100-digit number)
98999359869737871565…14706337870090076159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.899 Γ— 10⁹⁹(100-digit number)
98999359869737871565…14706337870090076161
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
1.979 Γ— 10¹⁰⁰(101-digit number)
19799871973947574313…29412675740180152319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.979 Γ— 10¹⁰⁰(101-digit number)
19799871973947574313…29412675740180152321
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
3.959 Γ— 10¹⁰⁰(101-digit number)
39599743947895148626…58825351480360304639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.959 Γ— 10¹⁰⁰(101-digit number)
39599743947895148626…58825351480360304641
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
7.919 Γ— 10¹⁰⁰(101-digit number)
79199487895790297252…17650702960720609279
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 2996263

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 52152a6c4aa1777a13024f6163196fa20fcd45ac0ba25c134a9a2227a05da0dd

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 #2,996,263 on Chainz β†—
Circulating Supply:57,895,422 XPMΒ·at block #6,831,407 Β· updates every 60s
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