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Block #120,306

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/17/2013, 2:14:10 AM Β· Difficulty 9.7496 Β· 6,705,118 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bbd97f6f8b5321621df0cdcafa261f59c891aea013e0803421c87dc5ee0463cb
View on Chainz β†—

Height

#120,306

Difficulty

9.749640

Transactions

1

Size

199 B

Version

2

Bits

09bfe869

Nonce

418,242

Timestamp

8/17/2013, 2:14:10 AM

Confirmations

6,705,118

Mined by

⛏️ P2SHAGELmJR6aPRjt3Z8ALYc9YsGpGUuQ4Rhjr

Merkle Root

fb390952ad8482a01091b6f6d7a848bbff2cec0b71fe1a282b253411787cdd19
Transactions (1)
Coinbasefb390952ad8482…253411787cdd19
1 in β†’ 1 out10.5000 XPM109 B
AGELmJR6…UuQ4Rhjr
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.

2.883 Γ— 10⁹⁴(95-digit number)
28839697849858216468…34053588684694351119
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
2.883 Γ— 10⁹⁴(95-digit number)
28839697849858216468…34053588684694351119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.883 Γ— 10⁹⁴(95-digit number)
28839697849858216468…34053588684694351121
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
5.767 Γ— 10⁹⁴(95-digit number)
57679395699716432937…68107177369388702239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.767 Γ— 10⁹⁴(95-digit number)
57679395699716432937…68107177369388702241
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
1.153 Γ— 10⁹⁡(96-digit number)
11535879139943286587…36214354738777404479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.153 Γ— 10⁹⁡(96-digit number)
11535879139943286587…36214354738777404481
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
2.307 Γ— 10⁹⁡(96-digit number)
23071758279886573175…72428709477554808959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.307 Γ— 10⁹⁡(96-digit number)
23071758279886573175…72428709477554808961
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
4.614 Γ— 10⁹⁡(96-digit number)
46143516559773146350…44857418955109617919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.614 Γ— 10⁹⁡(96-digit number)
46143516559773146350…44857418955109617921
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.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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
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