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Home/Chain Registry/Block #1,557,442

Block #1,557,442

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/25/2016, 12:22:25 PM Β· Difficulty 10.6882 Β· 5,259,352 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a815898d36fc2fff7ebea5c2a6a55eacbe4f55f985306442e0f958b9757eedb6
View on Chainz β†—

Difficulty

10.688189

Transactions

1

Size

200 B

Version

2

Bits

0ab02d21

Nonce

615,722,865

Timestamp

4/25/2016, 12:22:25 PM

Confirmations

5,259,352

Merkle Root

005ea24deab3850d7e46f04b58adfcbeec45bd17f6aaa4a96d475edd7ddd5885
Transactions (1)
Coinbase005ea24deab385…475edd7ddd5885
1 in β†’ 1 out8.7400 XPM110 B
AZhWa9au…Yo7TLNdB
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.

3.847 Γ— 10⁹³(94-digit number)
38477645708985304507…17692820778938935980
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
3.847 Γ— 10⁹³(94-digit number)
38477645708985304507…17692820778938935979
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.847 Γ— 10⁹³(94-digit number)
38477645708985304507…17692820778938935981
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
7.695 Γ— 10⁹³(94-digit number)
76955291417970609015…35385641557877871959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.695 Γ— 10⁹³(94-digit number)
76955291417970609015…35385641557877871961
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
1.539 Γ— 10⁹⁴(95-digit number)
15391058283594121803…70771283115755743919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.539 Γ— 10⁹⁴(95-digit number)
15391058283594121803…70771283115755743921
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
3.078 Γ— 10⁹⁴(95-digit number)
30782116567188243606…41542566231511487839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.078 Γ— 10⁹⁴(95-digit number)
30782116567188243606…41542566231511487841
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
6.156 Γ— 10⁹⁴(95-digit number)
61564233134376487212…83085132463022975679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.156 Γ— 10⁹⁴(95-digit number)
61564233134376487212…83085132463022975681
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 1557442

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 a815898d36fc2fff7ebea5c2a6a55eacbe4f55f985306442e0f958b9757eedb6

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 #1,557,442 on Chainz β†—
Circulating Supply:57,778,388 XPMΒ·at block #6,816,793 Β· updates every 60s
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