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Home/Chain Registry/Block #1,533,414

Block #1,533,414

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/9/2016, 1:01:06 PM Β· Difficulty 10.6165 Β· 5,293,128 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b38d2752c5e05c732da44df5a3e9812a2ebba482b413dacce2a199255e3f34ee
View on Chainz β†—

Difficulty

10.616472

Transactions

1

Size

243 B

Version

2

Bits

0a9dd118

Nonce

415,362,104

Timestamp

4/9/2016, 1:01:06 PM

Confirmations

5,293,128

Merkle Root

e6d394eecfe8c0656f2b37fd580f9321a35b5cb5a5d3b93f495d67979e434f4d
Transactions (1)
Coinbasee6d394eecfe8c0…5d67979e434f4d
1 in β†’ 2 out8.8600 XPM152 B
AW7XpJLz…npEJgCfvALPu3s2c…EJXLjVFh
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.

3.057 Γ— 10⁹⁷(98-digit number)
30575806607169789484…15944417122514339840
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
3.057 Γ— 10⁹⁷(98-digit number)
30575806607169789484…15944417122514339839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.057 Γ— 10⁹⁷(98-digit number)
30575806607169789484…15944417122514339841
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
6.115 Γ— 10⁹⁷(98-digit number)
61151613214339578969…31888834245028679679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.115 Γ— 10⁹⁷(98-digit number)
61151613214339578969…31888834245028679681
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
1.223 Γ— 10⁹⁸(99-digit number)
12230322642867915793…63777668490057359359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.223 Γ— 10⁹⁸(99-digit number)
12230322642867915793…63777668490057359361
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
2.446 Γ— 10⁹⁸(99-digit number)
24460645285735831587…27555336980114718719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.446 Γ— 10⁹⁸(99-digit number)
24460645285735831587…27555336980114718721
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
4.892 Γ— 10⁹⁸(99-digit number)
48921290571471663175…55110673960229437439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.892 Γ— 10⁹⁸(99-digit number)
48921290571471663175…55110673960229437441
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 1533414

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 b38d2752c5e05c732da44df5a3e9812a2ebba482b413dacce2a199255e3f34ee

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 #1,533,414 on Chainz β†—
Circulating Supply:57,856,484 XPMΒ·at block #6,826,541 Β· updates every 60s
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