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Block #141,410

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/30/2013, 7:16:25 AM Β· Difficulty 9.8350 Β· 6,671,471 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0abb5a7746f2b11b267a2962db66b82fe4456527fff40636567d40df1e19353b
View on Chainz β†—

Height

#141,410

Difficulty

9.835018

Transactions

1

Size

198 B

Version

2

Bits

09d5c3c0

Nonce

139,282

Timestamp

8/30/2013, 7:16:25 AM

Confirmations

6,671,471

Mined by

⛏️ P2SHAKVWeAriNw95pyvDwPjKdiw6WPDCVyQ7Tr

Merkle Root

faaae3d30d9bc6ceb1bc8b1fdc47be248dfc82d444ece5edd2d6703a2e57d69d
Transactions (1)
Coinbasefaaae3d30d9bc6…d6703a2e57d69d
1 in β†’ 1 out10.3200 XPM109 B
AKVWeAri…DCVyQ7Tr
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.

1.395 Γ— 10⁹²(93-digit number)
13956240848529491046…64323921081851904399
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
1.395 Γ— 10⁹²(93-digit number)
13956240848529491046…64323921081851904399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.395 Γ— 10⁹²(93-digit number)
13956240848529491046…64323921081851904401
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
2.791 Γ— 10⁹²(93-digit number)
27912481697058982093…28647842163703808799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.791 Γ— 10⁹²(93-digit number)
27912481697058982093…28647842163703808801
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
5.582 Γ— 10⁹²(93-digit number)
55824963394117964187…57295684327407617599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.582 Γ— 10⁹²(93-digit number)
55824963394117964187…57295684327407617601
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
1.116 Γ— 10⁹³(94-digit number)
11164992678823592837…14591368654815235199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.116 Γ— 10⁹³(94-digit number)
11164992678823592837…14591368654815235201
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
2.232 Γ— 10⁹³(94-digit number)
22329985357647185675…29182737309630470399
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:57,747,079 XPMΒ·at block #6,812,880 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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