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Block #387,861

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/3/2014, 10:11:15 AM Β· Difficulty 10.4156 Β· 6,451,011 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
450e38a61c319d18a0639404d9f15457c272066021db061dfe3b79d42a3d66ee
View on Chainz β†—

Height

#387,861

Difficulty

10.415605

Transactions

1

Size

207 B

Version

2

Bits

0a6a651c

Nonce

547,763

Timestamp

2/3/2014, 10:11:15 AM

Confirmations

6,451,011

Merkle Root

265794791d80f57798d618d5f32d7eaac124270f8a8c490dc0f9d040ebd26db3
Transactions (1)
Coinbase265794791d80f5…f9d040ebd26db3
1 in β†’ 1 out9.2000 XPM116 B
AbwWkWZt…kawDhufa
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.

9.308 Γ— 10⁹⁢(97-digit number)
93081065038869115304…27368042716038528960
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
9.308 Γ— 10⁹⁢(97-digit number)
93081065038869115304…27368042716038528959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.308 Γ— 10⁹⁢(97-digit number)
93081065038869115304…27368042716038528961
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
1.861 Γ— 10⁹⁷(98-digit number)
18616213007773823060…54736085432077057919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.861 Γ— 10⁹⁷(98-digit number)
18616213007773823060…54736085432077057921
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
3.723 Γ— 10⁹⁷(98-digit number)
37232426015547646121…09472170864154115839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.723 Γ— 10⁹⁷(98-digit number)
37232426015547646121…09472170864154115841
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
7.446 Γ— 10⁹⁷(98-digit number)
74464852031095292243…18944341728308231679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.446 Γ— 10⁹⁷(98-digit number)
74464852031095292243…18944341728308231681
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
1.489 Γ— 10⁹⁸(99-digit number)
14892970406219058448…37888683456616463359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.489 Γ— 10⁹⁸(99-digit number)
14892970406219058448…37888683456616463361
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 387861

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 450e38a61c319d18a0639404d9f15457c272066021db061dfe3b79d42a3d66ee

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 #387,861 on Chainz β†—
Circulating Supply:57,955,242 XPMΒ·at block #6,838,871 Β· updates every 60s
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