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Home/Chain Registry/Block #1,178,264

Block #1,178,264

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/31/2015, 12:38:39 PM Β· Difficulty 10.9340 Β· 5,664,791 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b9a5c8f13bffeaa62f233b2d00fb68ae48910604b5ed9a47f3a52ede6b040972
View on Chainz β†—

Difficulty

10.934029

Transactions

2

Size

433 B

Version

2

Bits

0aef1c88

Nonce

262,985,647

Timestamp

7/31/2015, 12:38:39 PM

Confirmations

5,664,791

Merkle Root

136662a6b653c16928f3dbae6d9a280c749591fe6f8e3acfaa66670c3b895de7
Transactions (2)
Coinbase630f160b7aa431…fb9a14d9256110
1 in β†’ 1 out8.3600 XPM116 B
AJCEY9yy…tg97E6zm
0ad7cbb8f6d846…72cbe0b94ca292
1 in β†’ 2 out3768.6223 XPM226 B
APwiG1jQ…mkUcTowUAQ539rFh…XyFao7mE
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.

2.352 Γ— 10⁹⁢(97-digit number)
23524981198092156512…54829066470191127040
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
2.352 Γ— 10⁹⁢(97-digit number)
23524981198092156512…54829066470191127039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.352 Γ— 10⁹⁢(97-digit number)
23524981198092156512…54829066470191127041
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
4.704 Γ— 10⁹⁢(97-digit number)
47049962396184313025…09658132940382254079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.704 Γ— 10⁹⁢(97-digit number)
47049962396184313025…09658132940382254081
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
9.409 Γ— 10⁹⁢(97-digit number)
94099924792368626050…19316265880764508159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.409 Γ— 10⁹⁢(97-digit number)
94099924792368626050…19316265880764508161
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
1.881 Γ— 10⁹⁷(98-digit number)
18819984958473725210…38632531761529016319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.881 Γ— 10⁹⁷(98-digit number)
18819984958473725210…38632531761529016321
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
3.763 Γ— 10⁹⁷(98-digit number)
37639969916947450420…77265063523058032639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.763 Γ— 10⁹⁷(98-digit number)
37639969916947450420…77265063523058032641
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 1178264

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 b9a5c8f13bffeaa62f233b2d00fb68ae48910604b5ed9a47f3a52ede6b040972

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 #1,178,264 on Chainz β†—
Circulating Supply:57,988,798 XPMΒ·at block #6,843,054 Β· updates every 60s
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