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Block #292,871

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/4/2013, 12:03:39 AM Β· Difficulty 9.9904 Β· 6,511,040 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0c684844c854435e122be6f8c4d12ff03f2473a8009b8e0f1a17c5c36eb275fb
View on Chainz β†—

Height

#292,871

Difficulty

9.990422

Transactions

2

Size

573 B

Version

2

Bits

09fd8c51

Nonce

14,776

Timestamp

12/4/2013, 12:03:39 AM

Confirmations

6,511,040

Mined by

⛏️ P2SHAGssgv8CenT6oWQcceq6rFxSyqzT3wunSb

Merkle Root

6ed7d40b13485183b6d7a3d8e965a4f0802ef151a03839a0057207494f9cd71b
Transactions (2)
Coinbase6a4acd20804716…153febd3bf95a0
1 in β†’ 1 out10.0100 XPM109 B
AGssgv8C…zT3wunSb
2815179fe50e26…f7e64314051ba2
2 in β†’ 2 out5239.6665 XPM374 B
AN84xATi…q7JYCxkMAVsQLh29…qkTcK5J1
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.

1.342 Γ— 10⁹⁴(95-digit number)
13422318245820001857…86851729892528038399
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
1.342 Γ— 10⁹⁴(95-digit number)
13422318245820001857…86851729892528038399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.342 Γ— 10⁹⁴(95-digit number)
13422318245820001857…86851729892528038401
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
2.684 Γ— 10⁹⁴(95-digit number)
26844636491640003715…73703459785056076799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.684 Γ— 10⁹⁴(95-digit number)
26844636491640003715…73703459785056076801
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
5.368 Γ— 10⁹⁴(95-digit number)
53689272983280007430…47406919570112153599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.368 Γ— 10⁹⁴(95-digit number)
53689272983280007430…47406919570112153601
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
1.073 Γ— 10⁹⁡(96-digit number)
10737854596656001486…94813839140224307199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.073 Γ— 10⁹⁡(96-digit number)
10737854596656001486…94813839140224307201
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
2.147 Γ— 10⁹⁡(96-digit number)
21475709193312002972…89627678280448614399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.147 Γ— 10⁹⁡(96-digit number)
21475709193312002972…89627678280448614401
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:57,675,335 XPMΒ·at block #6,803,910 Β· updates every 60s
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