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Block #142,829

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/31/2013, 5:32:56 AM Β· Difficulty 9.8377 Β· 6,664,327 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b1c282450582045f1b2d958df8570f9a734395050517f40c11fdb94cc4de39c9
View on Chainz β†—

Height

#142,829

Difficulty

9.837740

Transactions

1

Size

197 B

Version

2

Bits

09d67621

Nonce

245,934

Timestamp

8/31/2013, 5:32:56 AM

Confirmations

6,664,327

Mined by

⛏️ P2SHAN7XEitUUuigurw1EkSj72AqF71M2iWp4h

Merkle Root

a0e877fa64a848fea91b9e4ed0151e7f6b563a697ceabe1e4be49b3b46079ff2
Transactions (1)
Coinbasea0e877fa64a848…e49b3b46079ff2
1 in β†’ 1 out10.3200 XPM109 B
AN7XEitU…1M2iWp4h
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.

4.623 Γ— 10⁹⁰(91-digit number)
46237444050593236817…72220816035842506999
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
4.623 Γ— 10⁹⁰(91-digit number)
46237444050593236817…72220816035842506999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.623 Γ— 10⁹⁰(91-digit number)
46237444050593236817…72220816035842507001
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
9.247 Γ— 10⁹⁰(91-digit number)
92474888101186473634…44441632071685013999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.247 Γ— 10⁹⁰(91-digit number)
92474888101186473634…44441632071685014001
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
1.849 Γ— 10⁹¹(92-digit number)
18494977620237294726…88883264143370027999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.849 Γ— 10⁹¹(92-digit number)
18494977620237294726…88883264143370028001
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
3.698 Γ— 10⁹¹(92-digit number)
36989955240474589453…77766528286740055999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.698 Γ— 10⁹¹(92-digit number)
36989955240474589453…77766528286740056001
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
7.397 Γ— 10⁹¹(92-digit number)
73979910480949178907…55533056573480111999
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:57,701,255 XPMΒ·at block #6,807,155 Β· updates every 60s
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