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Block #189,772

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/2/2013, 12:54:15 AM Β· Difficulty 9.8738 Β· 6,613,899 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
93ce558ef9e0a999d92c6203821f637d9bedccc09bd1da5cc39bc9f0e9c70682
View on Chainz β†—

Height

#189,772

Difficulty

9.873796

Transactions

2

Size

1.25 KB

Version

2

Bits

09dfb118

Nonce

14,783

Timestamp

10/2/2013, 12:54:15 AM

Confirmations

6,613,899

Mined by

⛏️ P2SHAbJsT1MFiTkk7HZiVSZy3MgHLJpF3oUXHW

Merkle Root

13b5ef7e7608ad9a13f4c29815a7e7aabb1b8107a32fb30a632fe4ce80db381d
Transactions (2)
Coinbase8aff32fe1bf290…6169eeef88d0de
1 in β†’ 1 out10.2600 XPM109 B
AbJsT1MF…pF3oUXHW
5f9b0fb917c4a6…c0a7b993359122
7 in β†’ 1 out15.9253 XPM1.05 KB
AdJ1zbJE…R5kA3WZj
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.

7.876 Γ— 10⁹⁰(91-digit number)
78760845849729047179…87182153327263383039
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
7.876 Γ— 10⁹⁰(91-digit number)
78760845849729047179…87182153327263383039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.876 Γ— 10⁹⁰(91-digit number)
78760845849729047179…87182153327263383041
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
1.575 Γ— 10⁹¹(92-digit number)
15752169169945809435…74364306654526766079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.575 Γ— 10⁹¹(92-digit number)
15752169169945809435…74364306654526766081
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
3.150 Γ— 10⁹¹(92-digit number)
31504338339891618871…48728613309053532159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.150 Γ— 10⁹¹(92-digit number)
31504338339891618871…48728613309053532161
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
6.300 Γ— 10⁹¹(92-digit number)
63008676679783237743…97457226618107064319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.300 Γ— 10⁹¹(92-digit number)
63008676679783237743…97457226618107064321
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
1.260 Γ— 10⁹²(93-digit number)
12601735335956647548…94914453236214128639
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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
Cross-reference on Chainz Explorer
Circulating Supply:57,673,405 XPMΒ·at block #6,803,670 Β· updates every 60s
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