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Home/Chain Registry/Block #1,534,553

Block #1,534,553

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/10/2016, 7:57:17 AM Β· Difficulty 10.6169 Β· 5,292,701 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fc086b35e6a204eb5ff6c00cb428169a67ee4d6676ee2497a7d2726b4b45483a
View on Chainz β†—

Difficulty

10.616900

Transactions

1

Size

243 B

Version

2

Bits

0a9ded29

Nonce

90,802,392

Timestamp

4/10/2016, 7:57:17 AM

Confirmations

5,292,701

Merkle Root

348414312569336852a24a6212d91a9d760c801e2adeaf5978a746b14dfbc04d
Transactions (1)
Coinbase34841431256933…a746b14dfbc04d
1 in β†’ 2 out8.8600 XPM152 B
AJgZBh3x…9DpUcwi5ALPu3s2c…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.

3.791 Γ— 10⁹⁢(97-digit number)
37919290897799619218…37996280014478530560
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
3.791 Γ— 10⁹⁢(97-digit number)
37919290897799619218…37996280014478530559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.791 Γ— 10⁹⁢(97-digit number)
37919290897799619218…37996280014478530561
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
7.583 Γ— 10⁹⁢(97-digit number)
75838581795599238437…75992560028957061119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.583 Γ— 10⁹⁢(97-digit number)
75838581795599238437…75992560028957061121
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
1.516 Γ— 10⁹⁷(98-digit number)
15167716359119847687…51985120057914122239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.516 Γ— 10⁹⁷(98-digit number)
15167716359119847687…51985120057914122241
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
3.033 Γ— 10⁹⁷(98-digit number)
30335432718239695374…03970240115828244479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.033 Γ— 10⁹⁷(98-digit number)
30335432718239695374…03970240115828244481
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
6.067 Γ— 10⁹⁷(98-digit number)
60670865436479390749…07940480231656488959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.067 Γ— 10⁹⁷(98-digit number)
60670865436479390749…07940480231656488961
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 1534553

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 fc086b35e6a204eb5ff6c00cb428169a67ee4d6676ee2497a7d2726b4b45483a

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 #1,534,553 on Chainz β†—
Circulating Supply:57,862,135 XPMΒ·at block #6,827,253 Β· updates every 60s
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