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Block #2,479,054

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/18/2018, 4:33:59 PM Β· Difficulty 10.9658 Β· 4,360,721 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
022649dc82c1ef015a02fd8dc24e716316acac4145d38c0a1b2ca099778433d8
View on Chainz β†—

Difficulty

10.965806

Transactions

2

Size

392 B

Version

2

Bits

0af73f15

Nonce

1,144,907,715

Timestamp

1/18/2018, 4:33:59 PM

Confirmations

4,360,721

Merkle Root

ba413781869fd515102313dd1a2759aa90db9456573f5fd10ab2925f3f9ce7f6
Transactions (2)
Coinbase1117812a972921…20e7e2e72294b4
1 in β†’ 1 out8.3100 XPM109 B
AbMdFE5q…XZJkG3NT
66b077d209fa3e…38df09f6e508a9
1 in β†’ 2 out8.3000 XPM193 B
AN24acsN…j8WmedDvATDSXsmP…JYSc3iUt
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.

4.858 Γ— 10⁹⁴(95-digit number)
48580172045227738141…21275293059272896000
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
4.858 Γ— 10⁹⁴(95-digit number)
48580172045227738141…21275293059272895999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.858 Γ— 10⁹⁴(95-digit number)
48580172045227738141…21275293059272896001
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
9.716 Γ— 10⁹⁴(95-digit number)
97160344090455476282…42550586118545791999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.716 Γ— 10⁹⁴(95-digit number)
97160344090455476282…42550586118545792001
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
1.943 Γ— 10⁹⁡(96-digit number)
19432068818091095256…85101172237091583999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.943 Γ— 10⁹⁡(96-digit number)
19432068818091095256…85101172237091584001
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
3.886 Γ— 10⁹⁡(96-digit number)
38864137636182190512…70202344474183167999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.886 Γ— 10⁹⁡(96-digit number)
38864137636182190512…70202344474183168001
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
7.772 Γ— 10⁹⁡(96-digit number)
77728275272364381025…40404688948366335999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.772 Γ— 10⁹⁡(96-digit number)
77728275272364381025…40404688948366336001
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 2479054

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 022649dc82c1ef015a02fd8dc24e716316acac4145d38c0a1b2ca099778433d8

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 #2,479,054 on Chainz β†—
Circulating Supply:57,962,490 XPMΒ·at block #6,839,774 Β· updates every 60s
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