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Home/Chain Registry/Block #1,110,037

Block #1,110,037

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/16/2015, 12:27:12 PM Β· Difficulty 10.8658 Β· 5,702,379 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
badf3325d0e838cadc57eb92f7828f73e4b0b4aaf559f91c88ff6f5b8d95ab6c
View on Chainz β†—

Difficulty

10.865834

Transactions

1

Size

201 B

Version

2

Bits

0adda74f

Nonce

771,353,289

Timestamp

6/16/2015, 12:27:12 PM

Confirmations

5,702,379

Merkle Root

e832adda2003be82ee8fe77a7df94a88b52405c8a218a7a86742a13b280e29a5
Transactions (1)
Coinbasee832adda2003be…42a13b280e29a5
1 in β†’ 1 out8.4600 XPM110 B
AJYzmJxx…GVDfUn9q
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.

7.794 Γ— 10⁹⁢(97-digit number)
77945977344313621520…71927226157472655360
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
7.794 Γ— 10⁹⁢(97-digit number)
77945977344313621520…71927226157472655359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.794 Γ— 10⁹⁢(97-digit number)
77945977344313621520…71927226157472655361
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
1.558 Γ— 10⁹⁷(98-digit number)
15589195468862724304…43854452314945310719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.558 Γ— 10⁹⁷(98-digit number)
15589195468862724304…43854452314945310721
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
3.117 Γ— 10⁹⁷(98-digit number)
31178390937725448608…87708904629890621439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.117 Γ— 10⁹⁷(98-digit number)
31178390937725448608…87708904629890621441
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
6.235 Γ— 10⁹⁷(98-digit number)
62356781875450897216…75417809259781242879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.235 Γ— 10⁹⁷(98-digit number)
62356781875450897216…75417809259781242881
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
1.247 Γ— 10⁹⁸(99-digit number)
12471356375090179443…50835618519562485759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.247 Γ— 10⁹⁸(99-digit number)
12471356375090179443…50835618519562485761
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 1110037

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 badf3325d0e838cadc57eb92f7828f73e4b0b4aaf559f91c88ff6f5b8d95ab6c

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 #1,110,037 on Chainz β†—
Circulating Supply:57,743,356 XPMΒ·at block #6,812,415 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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