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Block #1,512,790

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/26/2016, 7:45:50 AM Β· Difficulty 10.6038 Β· 5,302,033 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
45db50032ea83f94ee5cdf439188df1c56ef9b3c7fca828c1d593143d0eb9c61
View on Chainz β†—

Difficulty

10.603824

Transactions

1

Size

244 B

Version

2

Bits

0a9a942e

Nonce

132,025,916

Timestamp

3/26/2016, 7:45:50 AM

Confirmations

5,302,033

Merkle Root

afb40c471e43ac4ec8ef8a4ad61e3f17ccdabc8b409f0974e93bd3b06116562c
Transactions (1)
Coinbaseafb40c471e43ac…3bd3b06116562c
1 in β†’ 2 out8.8800 XPM152 B
AXZf8xqq…hQwCQgXtALPu3s2c…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.

1.158 Γ— 10⁹⁹(100-digit number)
11583010863396392831…66145269895242383360
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
1.158 Γ— 10⁹⁹(100-digit number)
11583010863396392831…66145269895242383359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.158 Γ— 10⁹⁹(100-digit number)
11583010863396392831…66145269895242383361
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
2.316 Γ— 10⁹⁹(100-digit number)
23166021726792785663…32290539790484766719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.316 Γ— 10⁹⁹(100-digit number)
23166021726792785663…32290539790484766721
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
4.633 Γ— 10⁹⁹(100-digit number)
46332043453585571326…64581079580969533439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.633 Γ— 10⁹⁹(100-digit number)
46332043453585571326…64581079580969533441
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
9.266 Γ— 10⁹⁹(100-digit number)
92664086907171142652…29162159161939066879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.266 Γ— 10⁹⁹(100-digit number)
92664086907171142652…29162159161939066881
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
1.853 Γ— 10¹⁰⁰(101-digit number)
18532817381434228530…58324318323878133759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.853 Γ— 10¹⁰⁰(101-digit number)
18532817381434228530…58324318323878133761
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 1512790

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 45db50032ea83f94ee5cdf439188df1c56ef9b3c7fca828c1d593143d0eb9c61

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 #1,512,790 on Chainz β†—
Circulating Supply:57,762,672 XPMΒ·at block #6,814,822 Β· updates every 60s
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