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Block #385,667

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/1/2014, 10:48:12 PM Β· Difficulty 10.4064 Β· 6,409,731 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
82dda4bc4c535d6060545bd3888f9c1ae1d0f709aa882bc86a108c376b0c069a
View on Chainz β†—

Height

#385,667

Difficulty

10.406439

Transactions

1

Size

209 B

Version

2

Bits

0a680c64

Nonce

105,170

Timestamp

2/1/2014, 10:48:12 PM

Confirmations

6,409,731

Mined by

⛏️ P2SHAW6FdqAF2QFTdoj8WBd1FEKDKLmbtgXE2r

Merkle Root

b275f3bfd02f19ae47579cb2c336c31c4adbe468a097716c7c227fb61ca11a25
Transactions (1)
Coinbaseb275f3bfd02f19…227fb61ca11a25
1 in β†’ 1 out9.2200 XPM118 B
AW6FdqAF…mbtgXE2r
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.

3.192 Γ— 10⁹⁷(98-digit number)
31925237575263848660…87667045284741850319
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
3.192 Γ— 10⁹⁷(98-digit number)
31925237575263848660…87667045284741850319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.192 Γ— 10⁹⁷(98-digit number)
31925237575263848660…87667045284741850321
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
6.385 Γ— 10⁹⁷(98-digit number)
63850475150527697320…75334090569483700639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.385 Γ— 10⁹⁷(98-digit number)
63850475150527697320…75334090569483700641
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
1.277 Γ— 10⁹⁸(99-digit number)
12770095030105539464…50668181138967401279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.277 Γ— 10⁹⁸(99-digit number)
12770095030105539464…50668181138967401281
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
2.554 Γ— 10⁹⁸(99-digit number)
25540190060211078928…01336362277934802559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.554 Γ— 10⁹⁸(99-digit number)
25540190060211078928…01336362277934802561
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
5.108 Γ— 10⁹⁸(99-digit number)
51080380120422157856…02672724555869605119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.108 Γ— 10⁹⁸(99-digit number)
51080380120422157856…02672724555869605121
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.021 Γ— 10⁹⁹(100-digit number)
10216076024084431571…05345449111739210239
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,607,244 XPMΒ·at block #6,795,397 Β· updates every 60s
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