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Home/Chain Registry/Block #1,081,367

Block #1,081,367

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/29/2015, 1:19:15 PM Β· Difficulty 10.7651 Β· 5,745,756 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8f03f66ea4c8cc9f305a2d31eec21d5be93c13891aa48280e3c99477150acfe6
View on Chainz β†—

Difficulty

10.765129

Transactions

1

Size

208 B

Version

2

Bits

0ac3df78

Nonce

97,602,070

Timestamp

5/29/2015, 1:19:15 PM

Confirmations

5,745,756

Merkle Root

f3ad0b5f5e3801c974821baaa6c0b69461e808fe18cd9b42f711fd76e07c6c2f
Transactions (1)
Coinbasef3ad0b5f5e3801…11fd76e07c6c2f
1 in β†’ 1 out8.6200 XPM116 B
ANSXnLY2…Sd25TjkD
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.

3.931 Γ— 10⁹⁸(99-digit number)
39317771218912194139…35818154011963023360
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
3.931 Γ— 10⁹⁸(99-digit number)
39317771218912194139…35818154011963023359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.931 Γ— 10⁹⁸(99-digit number)
39317771218912194139…35818154011963023361
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
7.863 Γ— 10⁹⁸(99-digit number)
78635542437824388278…71636308023926046719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.863 Γ— 10⁹⁸(99-digit number)
78635542437824388278…71636308023926046721
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
1.572 Γ— 10⁹⁹(100-digit number)
15727108487564877655…43272616047852093439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.572 Γ— 10⁹⁹(100-digit number)
15727108487564877655…43272616047852093441
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
3.145 Γ— 10⁹⁹(100-digit number)
31454216975129755311…86545232095704186879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.145 Γ— 10⁹⁹(100-digit number)
31454216975129755311…86545232095704186881
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
6.290 Γ— 10⁹⁹(100-digit number)
62908433950259510622…73090464191408373759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.290 Γ— 10⁹⁹(100-digit number)
62908433950259510622…73090464191408373761
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.258 Γ— 10¹⁰⁰(101-digit number)
12581686790051902124…46180928382816747519
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 1081367

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 8f03f66ea4c8cc9f305a2d31eec21d5be93c13891aa48280e3c99477150acfe6

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 #1,081,367 on Chainz β†—
Circulating Supply:57,861,165 XPMΒ·at block #6,827,122 Β· updates every 60s
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