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Block #263,245

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/17/2013, 3:19:18 PM Β· Difficulty 9.9667 Β· 6,544,075 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1e00eadb8dad56589b77c34596dbc8774984f15667565e98a22d8f9caaf64050
View on Chainz β†—

Height

#263,245

Difficulty

9.966680

Transactions

2

Size

389 B

Version

2

Bits

09f77855

Nonce

77,906

Timestamp

11/17/2013, 3:19:18 PM

Confirmations

6,544,075

Mined by

⛏️ P2SHARdDiuG8TYpd2wtV15aZGy5J6Lwggxf9Qh

Merkle Root

9f84a413c862a0da790ab0733eef3d7cb31ef9035b1b2cf2c63850744e9eb92e
Transactions (2)
Coinbase71c63d5258a7f1…52c6892922d066
1 in β†’ 1 out10.0601 XPM109 B
ARdDiuG8…wggxf9Qh
dbf23fd6b8d42b…bbbb88784e7f14
1 in β†’ 1 out161.4613 XPM191 B
AcUKPiDe…4rznYsnA
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.

1.865 Γ— 10⁹³(94-digit number)
18654900180165594031…24871820964253766479
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
1.865 Γ— 10⁹³(94-digit number)
18654900180165594031…24871820964253766479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.865 Γ— 10⁹³(94-digit number)
18654900180165594031…24871820964253766481
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
3.730 Γ— 10⁹³(94-digit number)
37309800360331188062…49743641928507532959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.730 Γ— 10⁹³(94-digit number)
37309800360331188062…49743641928507532961
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
7.461 Γ— 10⁹³(94-digit number)
74619600720662376124…99487283857015065919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.461 Γ— 10⁹³(94-digit number)
74619600720662376124…99487283857015065921
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
1.492 Γ— 10⁹⁴(95-digit number)
14923920144132475224…98974567714030131839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.492 Γ— 10⁹⁴(95-digit number)
14923920144132475224…98974567714030131841
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
2.984 Γ— 10⁹⁴(95-digit number)
29847840288264950449…97949135428060263679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.984 Γ— 10⁹⁴(95-digit number)
29847840288264950449…97949135428060263681
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:57,702,576 XPMΒ·at block #6,807,319 Β· updates every 60s
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