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Home/Chain Registry/Block #2,996,844

Block #2,996,844

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/5/2019, 3:11:24 PM Β· Difficulty 11.2582 Β· 3,846,201 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7bc1387230a3bb7453c3ad07cfb57180fab0306a5a86292caccbebe794d2c1b3
View on Chainz β†—

Difficulty

11.258173

Transactions

1

Size

201 B

Version

2

Bits

0b42179f

Nonce

1,379,290,868

Timestamp

1/5/2019, 3:11:24 PM

Confirmations

3,846,201

Merkle Root

75a24f9f337787748054744f0b186463551ecc68fe352a50c381c28b05ab54a9
Transactions (1)
Coinbase75a24f9f337787…81c28b05ab54a9
1 in β†’ 1 out7.8800 XPM110 B
AbXwmGxD…4XXYP765
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.

2.196 Γ— 10⁹⁸(99-digit number)
21962041710676515681…26595214163379486720
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
2.196 Γ— 10⁹⁸(99-digit number)
21962041710676515681…26595214163379486719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.196 Γ— 10⁹⁸(99-digit number)
21962041710676515681…26595214163379486721
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
4.392 Γ— 10⁹⁸(99-digit number)
43924083421353031363…53190428326758973439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.392 Γ— 10⁹⁸(99-digit number)
43924083421353031363…53190428326758973441
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
8.784 Γ— 10⁹⁸(99-digit number)
87848166842706062727…06380856653517946879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.784 Γ— 10⁹⁸(99-digit number)
87848166842706062727…06380856653517946881
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
1.756 Γ— 10⁹⁹(100-digit number)
17569633368541212545…12761713307035893759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.756 Γ— 10⁹⁹(100-digit number)
17569633368541212545…12761713307035893761
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
3.513 Γ— 10⁹⁹(100-digit number)
35139266737082425091…25523426614071787519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.513 Γ— 10⁹⁹(100-digit number)
35139266737082425091…25523426614071787521
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
7.027 Γ— 10⁹⁹(100-digit number)
70278533474164850182…51046853228143575039
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 2996844

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 7bc1387230a3bb7453c3ad07cfb57180fab0306a5a86292caccbebe794d2c1b3

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 #2,996,844 on Chainz β†—
Circulating Supply:57,988,717 XPMΒ·at block #6,843,044 Β· updates every 60s
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