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Block #365,816

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/19/2014, 12:17:57 AM Β· Difficulty 10.4261 Β· 6,445,170 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c64f79fbe29728fd84ee478778daaad36cd7ead259bf15f3bbc6c4e2f8160921
View on Chainz β†—

Height

#365,816

Difficulty

10.426064

Transactions

2

Size

689 B

Version

2

Bits

0a6d1285

Nonce

267,307

Timestamp

1/19/2014, 12:17:57 AM

Confirmations

6,445,170

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

65adb89e40a02738e41827add6da42a9900d6cf1711f36aa6770660763c68337
Transactions (2)
Coinbase9c32985b5a603e…3f3f527f8032c3
1 in β†’ 1 out9.2000 XPM110 B
AeKNrjNj…1NEq95Ta
112505c1cf61b6…4c60934b4d8708
3 in β†’ 1 out1.0305 XPM489 B
AZmddkh4…NazHJEG1
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.

1.578 Γ— 10⁹⁴(95-digit number)
15784214138254136889…77349166793679519999
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
1.578 Γ— 10⁹⁴(95-digit number)
15784214138254136889…77349166793679519999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.578 Γ— 10⁹⁴(95-digit number)
15784214138254136889…77349166793679520001
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
3.156 Γ— 10⁹⁴(95-digit number)
31568428276508273778…54698333587359039999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.156 Γ— 10⁹⁴(95-digit number)
31568428276508273778…54698333587359040001
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
6.313 Γ— 10⁹⁴(95-digit number)
63136856553016547556…09396667174718079999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.313 Γ— 10⁹⁴(95-digit number)
63136856553016547556…09396667174718080001
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
1.262 Γ— 10⁹⁡(96-digit number)
12627371310603309511…18793334349436159999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.262 Γ— 10⁹⁡(96-digit number)
12627371310603309511…18793334349436160001
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
2.525 Γ— 10⁹⁡(96-digit number)
25254742621206619022…37586668698872319999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.525 Γ— 10⁹⁡(96-digit number)
25254742621206619022…37586668698872320001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,731,991 XPMΒ·at block #6,810,985 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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