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Block #13,235

TWNLength 7β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/11/2013, 12:44:29 PM Β· Difficulty 7.7885 Β· 6,788,098 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5894b426431e73a09d45b7844eec65ef789c3667aa294e68d2d59b8fe17799cc
View on Chainz β†—

Height

#13,235

Difficulty

7.788467

Transactions

1

Size

197 B

Version

2

Bits

07c9d8fd

Nonce

1,742

Timestamp

7/11/2013, 12:44:29 PM

Confirmations

6,788,098

Mined by

⛏️ P2SHAM6VRLKvWNLUn43QLb3EuhPjXzByN91i1u

Merkle Root

7a83928a0f3960722289bf463e670670a03af66936a8e268048acadd764012ac
Transactions (1)
Coinbase7a83928a0f3960…8acadd764012ac
1 in β†’ 1 out16.4600 XPM109 B
AM6VRLKv…ByN91i1u
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.

5.491 Γ— 10⁹⁰(91-digit number)
54910048226574775387…60224781036092136999
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
5.491 Γ— 10⁹⁰(91-digit number)
54910048226574775387…60224781036092136999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.491 Γ— 10⁹⁰(91-digit number)
54910048226574775387…60224781036092137001
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
1.098 Γ— 10⁹¹(92-digit number)
10982009645314955077…20449562072184273999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.098 Γ— 10⁹¹(92-digit number)
10982009645314955077…20449562072184274001
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
2.196 Γ— 10⁹¹(92-digit number)
21964019290629910155…40899124144368547999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.196 Γ— 10⁹¹(92-digit number)
21964019290629910155…40899124144368548001
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
4.392 Γ— 10⁹¹(92-digit number)
43928038581259820310…81798248288737095999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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 7

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:57,654,733 XPMΒ·at block #6,801,332 Β· updates every 60s
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