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Block #146,402

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/2/2013, 11:57:13 AM Β· Difficulty 9.8475 Β· 6,663,320 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
864d10842f8e31f855ac3e59a3e9b17b5f0a9c4d62262966078f10e76016945d
View on Chainz β†—

Height

#146,402

Difficulty

9.847465

Transactions

1

Size

198 B

Version

2

Bits

09d8f370

Nonce

177,171

Timestamp

9/2/2013, 11:57:13 AM

Confirmations

6,663,320

Mined by

⛏️ P2SHAN7XEitUUuigurw1EkSj72AqF71M2iWp4h

Merkle Root

fa599c27560067b49b1e3afdcac8bafb5cb1a88cfa2f937b5b0c21e3c16a39f3
Transactions (1)
Coinbasefa599c27560067…0c21e3c16a39f3
1 in β†’ 1 out10.3000 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.

1.083 Γ— 10⁹³(94-digit number)
10830347224371105550…51382005461884785519
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
1.083 Γ— 10⁹³(94-digit number)
10830347224371105550…51382005461884785519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.083 Γ— 10⁹³(94-digit number)
10830347224371105550…51382005461884785521
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
2.166 Γ— 10⁹³(94-digit number)
21660694448742211101…02764010923769571039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.166 Γ— 10⁹³(94-digit number)
21660694448742211101…02764010923769571041
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
4.332 Γ— 10⁹³(94-digit number)
43321388897484422203…05528021847539142079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.332 Γ— 10⁹³(94-digit number)
43321388897484422203…05528021847539142081
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
8.664 Γ— 10⁹³(94-digit number)
86642777794968844406…11056043695078284159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.664 Γ— 10⁹³(94-digit number)
86642777794968844406…11056043695078284161
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
1.732 Γ— 10⁹⁴(95-digit number)
17328555558993768881…22112087390156568319
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:57,721,857 XPMΒ·at block #6,809,721 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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