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Block #286,267

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/30/2013, 8:02:12 PM Β· Difficulty 9.9854 Β· 6,526,201 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d72b4f936d92bbb598214637e551e7407bc4901cee5f0f9cbe7c70a31768c6de
View on Chainz β†—

Height

#286,267

Difficulty

9.985368

Transactions

1

Size

199 B

Version

2

Bits

09fc410f

Nonce

46,172

Timestamp

11/30/2013, 8:02:12 PM

Confirmations

6,526,201

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

c7a55e2d6b3123809e3cd6204d35e7c133276b20b26541dd823860028adc1490
Transactions (1)
Coinbasec7a55e2d6b3123…3860028adc1490
1 in β†’ 1 out10.0100 XPM109 B
AeKNrjNj…1NEq95Ta
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.

1.730 Γ— 10⁹⁴(95-digit number)
17301388681168419323…36420207504495030159
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
1.730 Γ— 10⁹⁴(95-digit number)
17301388681168419323…36420207504495030159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.730 Γ— 10⁹⁴(95-digit number)
17301388681168419323…36420207504495030161
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
3.460 Γ— 10⁹⁴(95-digit number)
34602777362336838647…72840415008990060319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.460 Γ— 10⁹⁴(95-digit number)
34602777362336838647…72840415008990060321
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
6.920 Γ— 10⁹⁴(95-digit number)
69205554724673677294…45680830017980120639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.920 Γ— 10⁹⁴(95-digit number)
69205554724673677294…45680830017980120641
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
1.384 Γ— 10⁹⁡(96-digit number)
13841110944934735458…91361660035960241279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.384 Γ— 10⁹⁡(96-digit number)
13841110944934735458…91361660035960241281
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
2.768 Γ— 10⁹⁡(96-digit number)
27682221889869470917…82723320071920482559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.768 Γ— 10⁹⁡(96-digit number)
27682221889869470917…82723320071920482561
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:57,743,770 XPMΒ·at block #6,812,467 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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