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Home/Chain Registry/Block #1,112,081

Block #1,112,081

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/17/2015, 4:31:50 AM Β· Difficulty 10.8917 Β· 5,714,513 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c3ba1a5b396132ea36256989a34cc7348a6bf81daa537c4d9d723c87db986f77
View on Chainz β†—

Difficulty

10.891748

Transactions

1

Size

200 B

Version

2

Bits

0ae4499b

Nonce

1,070,267,165

Timestamp

6/17/2015, 4:31:50 AM

Confirmations

5,714,513

Merkle Root

e4bb94dd3086f5ba7a54c2534556933c5b8536b6d0844af159a83e96ab3fc05d
Transactions (1)
Coinbasee4bb94dd3086f5…a83e96ab3fc05d
1 in β†’ 1 out8.4200 XPM110 B
AKxuFgMe…AyURYd7n
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.

9.276 Γ— 10⁹³(94-digit number)
92762750714123443404…58659504925763830100
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
9.276 Γ— 10⁹³(94-digit number)
92762750714123443404…58659504925763830099
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.276 Γ— 10⁹³(94-digit number)
92762750714123443404…58659504925763830101
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
1.855 Γ— 10⁹⁴(95-digit number)
18552550142824688680…17319009851527660199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.855 Γ— 10⁹⁴(95-digit number)
18552550142824688680…17319009851527660201
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
3.710 Γ— 10⁹⁴(95-digit number)
37105100285649377361…34638019703055320399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.710 Γ— 10⁹⁴(95-digit number)
37105100285649377361…34638019703055320401
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
7.421 Γ— 10⁹⁴(95-digit number)
74210200571298754723…69276039406110640799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.421 Γ— 10⁹⁴(95-digit number)
74210200571298754723…69276039406110640801
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
1.484 Γ— 10⁹⁡(96-digit number)
14842040114259750944…38552078812221281599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.484 Γ— 10⁹⁡(96-digit number)
14842040114259750944…38552078812221281601
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 1112081

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 c3ba1a5b396132ea36256989a34cc7348a6bf81daa537c4d9d723c87db986f77

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 #1,112,081 on Chainz β†—
Circulating Supply:57,856,904 XPMΒ·at block #6,826,593 Β· updates every 60s
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