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Block #189,028

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/1/2013, 1:39:41 PM Β· Difficulty 9.8719 Β· 6,615,286 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
65e4c92b9652bb8ea5373c6ad88c580d3f7f013c127018af02ce9225b52f7e42
View on Chainz β†—

Height

#189,028

Difficulty

9.871902

Transactions

1

Size

199 B

Version

2

Bits

09df34fb

Nonce

151,894

Timestamp

10/1/2013, 1:39:41 PM

Confirmations

6,615,286

Mined by

⛏️ P2SHAT3dRckguQx6f5eEEVjWX7iYBwiggfceho

Merkle Root

d26129bfd067d8af4e37b558c38115f8ec5dfe3deec347eabdca9bfeb3f7ed15
Transactions (1)
Coinbased26129bfd067d8…ca9bfeb3f7ed15
1 in β†’ 1 out10.2500 XPM109 B
AT3dRckg…iggfceho
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.

1.435 Γ— 10⁹⁴(95-digit number)
14351405045106443693…44120756926120827199
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
1.435 Γ— 10⁹⁴(95-digit number)
14351405045106443693…44120756926120827199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.435 Γ— 10⁹⁴(95-digit number)
14351405045106443693…44120756926120827201
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
2.870 Γ— 10⁹⁴(95-digit number)
28702810090212887386…88241513852241654399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.870 Γ— 10⁹⁴(95-digit number)
28702810090212887386…88241513852241654401
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
5.740 Γ— 10⁹⁴(95-digit number)
57405620180425774772…76483027704483308799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.740 Γ— 10⁹⁴(95-digit number)
57405620180425774772…76483027704483308801
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
1.148 Γ— 10⁹⁡(96-digit number)
11481124036085154954…52966055408966617599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.148 Γ— 10⁹⁡(96-digit number)
11481124036085154954…52966055408966617601
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
2.296 Γ— 10⁹⁡(96-digit number)
22962248072170309908…05932110817933235199
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:57,678,565 XPMΒ·at block #6,804,313 Β· updates every 60s
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