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Home/Chain Registry/Block #1,387,340

Block #1,387,340

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/27/2015, 12:09:05 PM Β· Difficulty 10.8134 Β· 5,429,532 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1adf51516dc1a317bfedec0443686e799e069c3c852f07fcbbb26161ff1853bc
View on Chainz β†—

Difficulty

10.813433

Transactions

1

Size

199 B

Version

2

Bits

0ad03d2b

Nonce

391,668,187

Timestamp

12/27/2015, 12:09:05 PM

Confirmations

5,429,532

Merkle Root

b1ac4f53850a018b37284462cb5b92e3735970201a2acbb201aa7ff54edabf17
Transactions (1)
Coinbaseb1ac4f53850a01…aa7ff54edabf17
1 in β†’ 1 out8.5400 XPM109 B
ALc5fxWX…bPp1XqWu
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.

8.146 Γ— 10⁹⁴(95-digit number)
81460074906918201799…83126016083672483200
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
8.146 Γ— 10⁹⁴(95-digit number)
81460074906918201799…83126016083672483199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.146 Γ— 10⁹⁴(95-digit number)
81460074906918201799…83126016083672483201
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
1.629 Γ— 10⁹⁡(96-digit number)
16292014981383640359…66252032167344966399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.629 Γ— 10⁹⁡(96-digit number)
16292014981383640359…66252032167344966401
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
3.258 Γ— 10⁹⁡(96-digit number)
32584029962767280719…32504064334689932799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.258 Γ— 10⁹⁡(96-digit number)
32584029962767280719…32504064334689932801
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
6.516 Γ— 10⁹⁡(96-digit number)
65168059925534561439…65008128669379865599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.516 Γ— 10⁹⁡(96-digit number)
65168059925534561439…65008128669379865601
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
1.303 Γ— 10⁹⁢(97-digit number)
13033611985106912287…30016257338759731199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.303 Γ— 10⁹⁢(97-digit number)
13033611985106912287…30016257338759731201
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 1387340

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 1adf51516dc1a317bfedec0443686e799e069c3c852f07fcbbb26161ff1853bc

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 #1,387,340 on Chainz β†—
Circulating Supply:57,779,014 XPMΒ·at block #6,816,871 Β· updates every 60s
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