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Home/Chain Registry/Block #2,947,561

Block #2,947,561

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/1/2018, 4:31:26 PM Β· Difficulty 11.3945 Β· 3,896,898 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fdf1e52c5f8c456a2e88684bd2facab1655567d66b621b5a5aee4cd930b1c46e
View on Chainz β†—

Difficulty

11.394461

Transactions

1

Size

200 B

Version

2

Bits

0b64fb6c

Nonce

168,522,744

Timestamp

12/1/2018, 4:31:26 PM

Confirmations

3,896,898

Merkle Root

9bea0e242114f32c61bed57de746931202719ae1c74db7e76d5d99db37ece488
Transactions (1)
Coinbase9bea0e242114f3…5d99db37ece488
1 in β†’ 1 out7.6900 XPM110 B
AUMQRepm…tAfKmdW1
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.

2.404 Γ— 10⁹⁴(95-digit number)
24049140666048279164…47863688069262704640
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
2.404 Γ— 10⁹⁴(95-digit number)
24049140666048279164…47863688069262704639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.404 Γ— 10⁹⁴(95-digit number)
24049140666048279164…47863688069262704641
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
4.809 Γ— 10⁹⁴(95-digit number)
48098281332096558329…95727376138525409279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.809 Γ— 10⁹⁴(95-digit number)
48098281332096558329…95727376138525409281
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
9.619 Γ— 10⁹⁴(95-digit number)
96196562664193116658…91454752277050818559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.619 Γ— 10⁹⁴(95-digit number)
96196562664193116658…91454752277050818561
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
1.923 Γ— 10⁹⁡(96-digit number)
19239312532838623331…82909504554101637119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.923 Γ— 10⁹⁡(96-digit number)
19239312532838623331…82909504554101637121
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
3.847 Γ— 10⁹⁡(96-digit number)
38478625065677246663…65819009108203274239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.847 Γ— 10⁹⁡(96-digit number)
38478625065677246663…65819009108203274241
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
7.695 Γ— 10⁹⁡(96-digit number)
76957250131354493326…31638018216406548479
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 2947561

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 fdf1e52c5f8c456a2e88684bd2facab1655567d66b621b5a5aee4cd930b1c46e

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 #2,947,561 on Chainz β†—
Circulating Supply:58,000,071 XPMΒ·at block #6,844,458 Β· updates every 60s
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